Daily Papers

Drug shortages pose critical risks to patient care and healthcare systems worldwide, yet the effectiveness of regulatory interventions remains poorly understood due to information asymmetries in pharmaceutical supply chains. We propose ShortageSim, addresses this challenge by providing the first simulation framework that evaluates the impact of regulatory interventions on competition dynamics under information asymmetry. Using Large Language Model (LLM)-based agents, the framework models the strategic decisions of drug manufacturers and institutional buyers, in response to shortage alerts given by the regulatory agency. Unlike traditional game theory models that assume perfect rationality and complete information, ShortageSim simulates heterogeneous interpretations on regulatory announcements and the resulting decisions. Experiments on self-processed dataset of historical shortage events show that ShortageSim reduces the resolution lag for production disruption cases by up to 84\%, achieving closer alignment to real-world trajectories than the zero-shot baseline. Our framework confirms the effect of regulatory alert in addressing shortages and introduces a new method for understanding competition in multi-stage environments under uncertainty. We open-source ShortageSim and a dataset of 2,925 FDA shortage events, providing a novel framework for future research on policy design and testing in supply chains under information asymmetry.

We investigate factors contributing to LLM agents' success in competitive multi-agent environments, using auctions as a testbed where agents bid to maximize profit. The agents are equipped with bidding domain knowledge, distinct personas that reflect item preferences, and a memory of auction history. Our work extends the classic auction scenario by creating a realistic environment where multiple agents bid on houses, weighing aspects such as size, location, and budget to secure the most desirable homes at the lowest prices. Particularly, we investigate three key questions: (a) How does a persona influence an agent's behavior in a competitive setting? (b) Can an agent effectively profile its competitors' behavior during auctions? (c) How can persona profiling be leveraged to create an advantage using strategies such as theory of mind? Through a series of experiments, we analyze the behaviors of LLM agents and shed light on new findings. Our testbed, called HARBOR, offers a valuable platform for deepening our understanding of multi-agent workflows in competitive environments.

The emergence of in-context learning (ICL) is potentially attributed to two major abilities: task recognition (TR) for recognizing the task from demonstrations and utilizing pre-trained priors, and task learning (TL) for learning from demonstrations. However, relationships between the two abilities and how such relationships affect the emergence of ICL is unclear. In this paper, we take the first step by examining the pre-training dynamics of the emergence of ICL. With carefully designed metrics, we find that these two abilities are, in fact, competitive during pre-training. Moreover, we observe a strong negative correlation between the competition and ICL performance. Further analysis of common pre-training factors (i.e., model size, dataset size, and data curriculum) demonstrates possible ways to manage the competition. Based on these insights, we propose a simple yet effective method to better integrate these two abilities for ICL at inference time. Through adaptive ensemble learning, the performance of ICL can be significantly boosted, enabling two small models to outperform a larger one with more than twice the parameters. The code is available at https://github.com/RUCAIBox/Competitive-ICL.

Data imbalance is a common problem in machine learning that can have a critical effect on the performance of a model. Various solutions exist but their impact on the convergence of the learning dynamics is not understood. Here, we elucidate the significant negative impact of data imbalance on learning, showing that the learning curves for minority and majority classes follow sub-optimal trajectories when training with a gradient-based optimizer. This slowdown is related to the imbalance ratio and can be traced back to a competition between the optimization of different classes. Our main contribution is the analysis of the convergence of full-batch (GD) and stochastic gradient descent (SGD), and of variants that renormalize the contribution of each per-class gradient. We find that GD is not guaranteed to decrease the loss for each class but that this problem can be addressed by performing a per-class normalization of the gradient. With SGD, class imbalance has an additional effect on the direction of the gradients: the minority class suffers from a higher directional noise, which reduces the effectiveness of the per-class gradient normalization. Our findings not only allow us to understand the potential and limitations of strategies involving the per-class gradients, but also the reason for the effectiveness of previously used solutions for class imbalance such as oversampling.

Large Language Models (LLMs) have shown remarkable capabilities as autonomous agents, yet existing benchmarks either focus on single-agent tasks or are confined to narrow domains, failing to capture the dynamics of multi-agent coordination and competition. In this paper, we introduce MultiAgentBench, a comprehensive benchmark designed to evaluate LLM-based multi-agent systems across diverse, interactive scenarios. Our framework measures not only task completion but also the quality of collaboration and competition using novel, milestone-based key performance indicators. Moreover, we evaluate various coordination protocols (including star, chain, tree, and graph topologies) and innovative strategies such as group discussion and cognitive planning. Notably, gpt-4o-mini reaches the average highest task score, graph structure performs the best among coordination protocols in the research scenario, and cognitive planning improves milestone achievement rates by 3%. Code and datasets are public available at https://github.com/MultiagentBench/MARBLE.

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.

Self-attention (SA) has become the cornerstone of modern vision backbones for its powerful expressivity over traditional Convolutions (Conv). However, its quadratic complexity remains a critical bottleneck for practical applications. Given that Conv offers linear complexity and strong visual priors, continuing efforts have been made to promote the renaissance of Conv. However, a persistent performance chasm remains, highlighting that these modernizations have not yet captured the intrinsic expressivity that defines SA. In this paper, we re-examine the design of the CNNs, directed by a key question: what principles give SA its edge over Conv? As a result, we reveal two fundamental insights that challenge the long-standing design intuitions in prior research (e.g., Receptive field). The two findings are: (1) Adaptive routing: SA dynamically regulates positional information flow according to semantic content, whereas Conv employs static kernels uniformly across all positions. (2) Lateral inhibition: SA induces score competition among token weighting, effectively suppressing redundancy and sharpening representations, whereas Conv filters lack such inhibitory dynamics and exhibit considerable redundancy. Based on this, we propose Attentive Convolution (ATConv), a principled reformulation of the convolutional operator that intrinsically injects these principles. Interestingly, with only 3times3 kernels, ATConv consistently outperforms various SA mechanisms in fundamental vision tasks. Building on ATConv, we introduce AttNet, a CNN family that can attain 84.4\% ImageNet-1K Top-1 accuracy with only 27M parameters. In diffusion-based image generation, replacing all SA with the proposed 3times 3 ATConv in SiT-XL/2 reduces ImageNet FID by 0.15 in 400k steps with faster sampling. Code is available at: github.com/price112/Attentive-Convolution.

Large language models (LLMs) are increasingly shaping how information is created and disseminated, from companies using them to craft persuasive advertisements, to election campaigns optimizing messaging to gain votes, to social media influencers boosting engagement. These settings are inherently competitive, with sellers, candidates, and influencers vying for audience approval, yet it remains poorly understood how competitive feedback loops influence LLM behavior. We show that optimizing LLMs for competitive success can inadvertently drive misalignment. Using simulated environments across these scenarios, we find that, 6.3% increase in sales is accompanied by a 14.0% rise in deceptive marketing; in elections, a 4.9% gain in vote share coincides with 22.3% more disinformation and 12.5% more populist rhetoric; and on social media, a 7.5% engagement boost comes with 188.6% more disinformation and a 16.3% increase in promotion of harmful behaviors. We call this phenomenon Moloch's Bargain for AI--competitive success achieved at the cost of alignment. These misaligned behaviors emerge even when models are explicitly instructed to remain truthful and grounded, revealing the fragility of current alignment safeguards. Our findings highlight how market-driven optimization pressures can systematically erode alignment, creating a race to the bottom, and suggest that safe deployment of AI systems will require stronger governance and carefully designed incentives to prevent competitive dynamics from undermining societal trust.

The rapid proliferation of Large Language Models (LLMs) and diverse specialized benchmarks necessitates a shift from fragmented, task-specific metrics to a holistic, competitive ranking system that effectively aggregates performance across multiple ability dimensions. Primarily using static scoring, current evaluation methods are fundamentally limited. They struggle to determine the proper mix ratio across diverse benchmarks, and critically, they fail to capture a model's dynamic competitive fitness or its vulnerability when confronted with sequential, high-stakes tasks. To address this, we introduce the novel Competitive Swiss-System Dynamics (CSD) framework. CSD simulates a multi-round, sequential contest where models are dynamically paired across a curated sequence of benchmarks based on their accumulated win-loss record. And Monte Carlo Simulation (N=100,000 iterations) is used to approximate the statistically robust Expected Win Score (E[S_m]), which eliminates the noise of random pairing and early-round luck. Furthermore, we implement a Failure Sensitivity Analysis by parameterizing the per-round elimination quantity (T_k), which allows us to profile models based on their risk appetite--distinguishing between robust generalists and aggressive specialists. We demonstrate that CSD provides a more nuanced and context-aware ranking than traditional aggregate scoring and static pairwise models, representing a vital step towards risk-informed, next-generation LLM evaluation.

As LLM agents advance, they are increasingly mediating economic decisions, ranging from product discovery to transactions, on behalf of users. Such applications promise benefits but also raise many questions about agent accountability and value for users. Addressing these questions requires understanding how agents behave in realistic market conditions. However, previous research has largely evaluated agents in constrained settings, such as single-task marketplaces (e.g., negotiation) or structured two-agent interactions. Real-world markets are fundamentally different: they require agents to handle diverse economic activities and coordinate within large, dynamic ecosystems where multiple agents with opaque behaviors may engage in open-ended dialogues. To bridge this gap, we investigate two-sided agentic marketplaces where Assistant agents represent consumers and Service agents represent competing businesses. To study these interactions safely, we develop Magentic-Marketplace-- a simulated environment where Assistants and Services can operate. This environment enables us to study key market dynamics: the utility agents achieve, behavioral biases, vulnerability to manipulation, and how search mechanisms shape market outcomes. Our experiments show that frontier models can approach optimal welfare-- but only under ideal search conditions. Performance degrades sharply with scale, and all models exhibit severe first-proposal bias, creating 10-30x advantages for response speed over quality. These findings reveal how behaviors emerge across market conditions, informing the design of fair and efficient agentic marketplaces.

The emergence of complex life on Earth is often attributed to the arms race that ensued from a huge number of organisms all competing for finite resources. We present an artificial intelligence research environment, inspired by the human game genre of MMORPGs (Massively Multiplayer Online Role-Playing Games, a.k.a. MMOs), that aims to simulate this setting in microcosm. As with MMORPGs and the real world alike, our environment is persistent and supports a large and variable number of agents. Our environment is well suited to the study of large-scale multiagent interaction: it requires that agents learn robust combat and navigation policies in the presence of large populations attempting to do the same. Baseline experiments reveal that population size magnifies and incentivizes the development of skillful behaviors and results in agents that outcompete agents trained in smaller populations. We further show that the policies of agents with unshared weights naturally diverge to fill different niches in order to avoid competition.

Common-pool resource governance requires users to cooperate and avoid overexploitation, but defection and free-riding often undermine cooperation. We model a human-environmental system that integrates dynamics of resource and users' strategies. The resource follows a logistic function that depends on natural growth rate, carrying capacity, and extraction rates of cooperators and defectors. The users' strategies evolve according to different processes that capture effects of payoff, resource, and noise. We analyze the feedback between resource availability and strategic adaptation, and explores the conditions for the emergence and maintenance of cooperation. We find different processes lead to different regimes of equilibrium solutions and resource levels depending on the parameter configuration and initial conditions. We also show that some processes can enhance the sustainability of the resource by making the users more responsive to the resource scarcity. The paper advances the understanding of human-environmental system and offers insights for resource governance policies and interventions.

This paper introduces a simulator designed for opinion dynamics researchers to model competing influences within social networks in the presence of LLM-based agents. By integrating established opinion dynamics principles with state-of-the-art LLMs, this tool enables the study of influence propagation and counter-misinformation strategies. The simulator is particularly valuable for researchers in social science, psychology, and operations research, allowing them to analyse societal phenomena without requiring extensive coding expertise. Additionally, the simulator will be openly available on GitHub, ensuring accessibility and adaptability for those who wish to extend its capabilities for their own research.

Computing stable partitions in hedonic games is a challenging task because there exist games in which stable outcomes do not exist. Even more, these No-instances can often be leveraged to prove computational hardness results. We make this impression rigorous in a dynamic model of cardinal hedonic games by providing meta theorems. These imply hardness of deciding about the possible or necessary convergence of deviation dynamics based on the mere existence of No-instances. Our results hold for additively separable, fractional, and modified fractional hedonic games (ASHGs, FHGs, and MFHGs). Moreover, they encompass essentially all reasonable stability notions based on single-agent deviations. In addition, we propose dynamics as a method to find individually rational and contractually individual stable (CIS) partitions in ASHGs. In particular, we find that CIS dynamics from the singleton partition possibly converge after a linear number of deviations but may require an exponential number of deviations in the worst case.

Through multi-agent competition, the simple objective of hide-and-seek, and standard reinforcement learning algorithms at scale, we find that agents create a self-supervised autocurriculum inducing multiple distinct rounds of emergent strategy, many of which require sophisticated tool use and coordination. We find clear evidence of six emergent phases in agent strategy in our environment, each of which creates a new pressure for the opposing team to adapt; for instance, agents learn to build multi-object shelters using moveable boxes which in turn leads to agents discovering that they can overcome obstacles using ramps. We further provide evidence that multi-agent competition may scale better with increasing environment complexity and leads to behavior that centers around far more human-relevant skills than other self-supervised reinforcement learning methods such as intrinsic motivation. Finally, we propose transfer and fine-tuning as a way to quantitatively evaluate targeted capabilities, and we compare hide-and-seek agents to both intrinsic motivation and random initialization baselines in a suite of domain-specific intelligence tests.

During 2023, two interesting results were proven about the limit behavior of game dynamics: First, it was shown that there is a game for which no dynamics converges to the Nash equilibria. Second, it was shown that the sink equilibria of a game adequately capture the limit behavior of natural game dynamics. These two results have created a need and opportunity to articulate a principled computational theory of the meaning of the game that is based on game dynamics. Given any game in normal form, and any prior distribution of play, we study the problem of computing the asymptotic behavior of a class of natural dynamics called the noisy replicator dynamics as a limit distribution over the sink equilibria of the game. When the prior distribution has pure strategy support, we prove this distribution can be computed efficiently, in near-linear time to the size of the best-response graph. When the distribution can be sampled -- for example, if it is the uniform distribution over all mixed strategy profiles -- we show through experiments that the limit distribution of reasonably large games can be estimated quite accurately through sampling and simulation.

The majority of online display ads are served through real-time bidding (RTB) --- each ad display impression is auctioned off in real-time when it is just being generated from a user visit. To place an ad automatically and optimally, it is critical for advertisers to devise a learning algorithm to cleverly bid an ad impression in real-time. Most previous works consider the bid decision as a static optimization problem of either treating the value of each impression independently or setting a bid price to each segment of ad volume. However, the bidding for a given ad campaign would repeatedly happen during its life span before the budget runs out. As such, each bid is strategically correlated by the constrained budget and the overall effectiveness of the campaign (e.g., the rewards from generated clicks), which is only observed after the campaign has completed. Thus, it is of great interest to devise an optimal bidding strategy sequentially so that the campaign budget can be dynamically allocated across all the available impressions on the basis of both the immediate and future rewards. In this paper, we formulate the bid decision process as a reinforcement learning problem, where the state space is represented by the auction information and the campaign's real-time parameters, while an action is the bid price to set. By modeling the state transition via auction competition, we build a Markov Decision Process framework for learning the optimal bidding policy to optimize the advertising performance in the dynamic real-time bidding environment. Furthermore, the scalability problem from the large real-world auction volume and campaign budget is well handled by state value approximation using neural networks.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

Competitions for shareable and limited resources have long been studied with strategic agents. In reality, agents often have to learn and maximize the rewards of the resources at the same time. To design an individualized competing policy, we model the competition between agents in a novel multi-player multi-armed bandit (MPMAB) setting where players are selfish and aim to maximize their own rewards. In addition, when several players pull the same arm, we assume that these players averagely share the arms' rewards by expectation. Under this setting, we first analyze the Nash equilibrium when arms' rewards are known. Subsequently, we propose a novel SelfishMPMAB with Averaging Allocation (SMAA) approach based on the equilibrium. We theoretically demonstrate that SMAA could achieve a good regret guarantee for each player when all players follow the algorithm. Additionally, we establish that no single selfish player can significantly increase their rewards through deviation, nor can they detrimentally affect other players' rewards without incurring substantial losses for themselves. We finally validate the effectiveness of the method in extensive synthetic experiments.

The deployment of ever-larger machine learning models reflects a growing consensus that the more expressive the modelx2013and the more data one has access tox2013the more one can improve performance. As models get deployed in a variety of real world scenarios, they inevitably face strategic environments. In this work, we consider the natural question of how the interplay of models and strategic interactions affects scaling laws. We find that strategic interactions can break the conventional view of scaling lawsx2013meaning that performance does not necessarily monotonically improve as models get larger and/ or more expressive (even with infinite data). We show the implications of this phenomenon in several contexts including strategic regression, strategic classification, and multi-agent reinforcement learning through examples of strategic environments in whichx2013by simply restricting the expressivity of one's model or policy classx2013one can achieve strictly better equilibrium outcomes. Motivated by these examples, we then propose a new paradigm for model-selection in games wherein an agent seeks to choose amongst different model classes to use as their action set in a game.

Competitive debate is a complex task of computational argumentation. Large Language Models (LLMs) suffer from hallucinations and lack competitiveness in this field. To address these challenges, we introduce Agent for Debate (Agent4Debate), a dynamic multi-agent framework based on LLMs designed to enhance their capabilities in competitive debate. Drawing inspiration from human behavior in debate preparation and execution, Agent4Debate employs a collaborative architecture where four specialized agents, involving Searcher, Analyzer, Writer, and Reviewer, dynamically interact and cooperate. These agents work throughout the debate process, covering multiple stages from initial research and argument formulation to rebuttal and summary. To comprehensively evaluate framework performance, we construct the Competitive Debate Arena, comprising 66 carefully selected Chinese debate motions. We recruit ten experienced human debaters and collect records of 200 debates involving Agent4Debate, baseline models, and humans. The evaluation employs the Debatrix automatic scoring system and professional human reviewers based on the established Debatrix-Elo and Human-Elo ranking. Experimental results indicate that the state-of-the-art Agent4Debate exhibits capabilities comparable to those of humans. Furthermore, ablation studies demonstrate the effectiveness of each component in the agent structure.

We initiate the study of statistical inference and A/B testing for first-price pacing equilibria (FPPE). The FPPE model captures the dynamics resulting from large-scale first-price auction markets where buyers use pacing-based budget management. Such markets arise in the context of internet advertising, where budgets are prevalent. We propose a statistical framework for the FPPE model, in which a limit FPPE with a continuum of items models the long-run steady-state behavior of the auction platform, and an observable FPPE consisting of a finite number of items provides the data to estimate primitives of the limit FPPE, such as revenue, Nash social welfare (a fair metric of efficiency), and other parameters of interest. We develop central limit theorems and asymptotically valid confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of our estimators. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Numerical simulations verify our central limit theorems, and empirical coverage rates for our confidence intervals agree with our theory.

Interpretability research aims to bridge the gap between empirical success and our scientific understanding of the inner workings of large language models (LLMs). However, most existing research focuses on analyzing a single mechanism, such as how models copy or recall factual knowledge. In this work, we propose a formulation of competition of mechanisms, which focuses on the interplay of multiple mechanisms instead of individual mechanisms and traces how one of them becomes dominant in the final prediction. We uncover how and where mechanisms compete within LLMs using two interpretability methods: logit inspection and attention modification. Our findings show traces of the mechanisms and their competition across various model components and reveal attention positions that effectively control the strength of certain mechanisms. Code: https://github.com/francescortu/comp-mech. Data: https://huggingface.co/datasets/francescortu/comp-mech.

While Large Language Models (LLMs) have demonstrated their proficiency in complex reasoning tasks, their performance in dynamic, interactive, and competitive scenarios - such as business strategy and stock market analysis - remains underexplored. To bridge this gap, we formally explore the dynamic reasoning capabilities of LLMs for decision-making in rapidly evolving environments. We introduce two game theory-based pilot challenges that mirror the complexities of real-world dynamic decision-making. These challenges are well-defined, enabling clear, controllable, and precise evaluation of LLMs' dynamic reasoning abilities. Through extensive experiments, we find that existing reasoning methods tend to falter in dynamic settings that require k-level thinking - a key concept not tackled by previous works. To address this, we propose a novel reasoning approach for LLMs, named "K-Level Reasoning". This approach adopts the perspective of rivals to recursively employ k-level thinking based on available historical information, which significantly improves the prediction accuracy of rivals' subsequent moves and informs more strategic decision-making. This research not only sets a robust quantitative benchmark for the assessment of dynamic reasoning but also markedly enhances the proficiency of LLMs in dynamic contexts.

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

In peer mechanisms, the competitors for a prize also determine who wins. Each competitor may be asked to rank, grade, or nominate peers for the prize. Since the prize can be valuable, such as financial aid, course grades, or an award at a conference, competitors may be tempted to manipulate the mechanism. We survey approaches to prevent or discourage the manipulation of peer mechanisms. We conclude our survey by identifying several important research challenges.

Large Language Models (LLMs) show significant potential in economic and strategic interactions, where communication via natural language is often prevalent. This raises key questions: Do LLMs behave rationally? Can they mimic human behavior? Do they tend to reach an efficient and fair outcome? What is the role of natural language in the strategic interaction? How do characteristics of the economic environment influence these dynamics? These questions become crucial concerning the economic and societal implications of integrating LLM-based agents into real-world data-driven systems, such as online retail platforms and recommender systems. While the ML community has been exploring the potential of LLMs in such multi-agent setups, varying assumptions, design choices and evaluation criteria across studies make it difficult to draw robust and meaningful conclusions. To address this, we introduce a benchmark for standardizing research on two-player, sequential, language-based games. Inspired by the economic literature, we define three base families of games with consistent parameterization, degrees of freedom and economic measures to evaluate agents' performance (self-gain), as well as the game outcome (efficiency and fairness). We develop an open-source framework for interaction simulation and analysis, and utilize it to collect a dataset of LLM vs. LLM interactions across numerous game configurations and an additional dataset of human vs. LLM interactions. Through extensive experimentation, we demonstrate how our framework and dataset can be used to: (i) compare the behavior of LLM-based agents to human players in various economic contexts; (ii) evaluate agents in both individual and collective performance measures; and (iii) quantify the effect of the economic characteristics of the environments on the behavior of agents.

Recent evidence suggests that the use of generative artificial intelligence reduces the diversity of content produced. In this work, we develop a game-theoretic model to explore the downstream consequences of content homogeneity when producers use generative AI to compete with one another. At equilibrium, players indeed produce content that is less diverse than optimal. However, stronger competition mitigates homogeneity and induces more diverse production. Perhaps more surprisingly, we show that a generative AI model that performs well in isolation (i.e., according to a benchmark) may fail to do so when faced with competition, and vice versa. We validate our results empirically by using language models to play Scattergories, a word game in which players are rewarded for producing answers that are both correct and unique. We discuss how the interplay between competition and homogeneity has implications for the development, evaluation, and use of generative AI.

Societies are complex. Properties of social systems can be explained by the interplay and weaving of individual actions. Incentives are key to understand people's choices and decisions. For instance, individual preferences of where to live may lead to the emergence of social segregation. In this paper, we combine Reinforcement Learning (RL) with Agent Based Models (ABM) in order to address the self-organizing dynamics of social segregation and explore the space of possibilities that emerge from considering different types of incentives. Our model promotes the creation of interdependencies and interactions among multiple agents of two different kinds that want to segregate from each other. For this purpose, agents use Deep Q-Networks to make decisions based on the rules of the Schelling Segregation model and the Predator-Prey model. Despite the segregation incentive, our experiments show that spatial integration can be achieved by establishing interdependencies among agents of different kinds. They also reveal that segregated areas are more probable to host older people than diverse areas, which attract younger ones. Through this work, we show that the combination of RL and ABMs can create an artificial environment for policy makers to observe potential and existing behaviors associated to incentives.

As Large Language Models (LLMs) integrate into our social and economic interactions, we need to deepen our understanding of how humans respond to LLMs opponents in strategic settings. We present the results of the first controlled monetarily-incentivised laboratory experiment looking at differences in human behaviour in a multi-player p-beauty contest against other humans and LLMs. We use a within-subject design in order to compare behaviour at the individual level. We show that, in this environment, human subjects choose significantly lower numbers when playing against LLMs than humans, which is mainly driven by the increased prevalence of `zero' Nash-equilibrium choices. This shift is mainly driven by subjects with high strategic reasoning ability. Subjects who play the zero Nash-equilibrium choice motivate their strategy by appealing to perceived LLM's reasoning ability and, unexpectedly, propensity towards cooperation. Our findings provide foundational insights into the multi-player human-LLM interaction in simultaneous choice games, uncover heterogeneities in both subjects' behaviour and beliefs about LLM's play when playing against them, and suggest important implications for mechanism design in mixed human-LLM systems.

Competitions play an invaluable role in the field of forecasting, as exemplified through the recent M4 competition. The competition received attention from both academics and practitioners and sparked discussions around the representativeness of the data for business forecasting. Several competitions featuring real-life business forecasting tasks on the Kaggle platform has, however, been largely ignored by the academic community. We believe the learnings from these competitions have much to offer to the forecasting community and provide a review of the results from six Kaggle competitions. We find that most of the Kaggle datasets are characterized by higher intermittence and entropy than the M-competitions and that global ensemble models tend to outperform local single models. Furthermore, we find the strong performance of gradient boosted decision trees, increasing success of neural networks for forecasting, and a variety of techniques for adapting machine learning models to the forecasting task.

We improve the framework of open games with agency by showing how the players' counterfactual analysis giving rise to Nash equilibria can be described in the dynamics of the game itself (hence diegetically), getting rid of devices such as equilibrium predicates. This new approach overlaps almost completely with the way gradient-based learners are specified and trained. Indeed, we show feedback propagation in games can be seen as a form of backpropagation, with a crucial difference explaining the distinctive character of the phenomenology of non-cooperative games. We outline a functorial construction of arena of games, show players form a subsystem over it, and prove that their 'fixpoint behaviours' are Nash equilibria.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

Coopetition refers to simultaneous cooperation and competition among actors wherein actors 'cooperate to grow the pie and compete to split it up.' Modern socio-technical systems are characterized by strategic coopetition wherein actors concomitantly cooperate to create value and compete to capture it. While conceptual modeling languages such as i* provide rich qualitative representations of strategic dependencies, they lack mechanisms for quantitative analysis of dynamic trade-offs. Conversely, classical game theory offers mathematical rigor but strips away contextual richness. This report bridges this gap by developing computational foundations that formalize two critical dimensions of coopetition: interdependence and complementarity. We ground interdependence in i* structural dependency analysis, translating depender-dependee-dependum relationships into quantitative interdependence coefficients via a structured translation framework. We formalize complementarity following Brandenburger and Nalebuff's Added Value concept, modeling synergistic value creation with validated parameterization. We integrate structural dependencies with bargaining power in value appropriation and introduce a game-theoretic formulation where Nash Equilibrium incorporates structural interdependence. Validation combines over 22,000 experimental trials across power and logarithmic specifications with the Samsung-Sony S-LCD joint venture (2004-2011). Under strict historical alignment scoring, logarithmic specifications achieve 58/60 compared to power functions (46/60), producing realistic 41% cooperation increases aligning with documented S-LCD patterns while power functions produce 166% increases exceeding realistic bounds. Statistical significance confirmed at p < 0.001, Cohen's d > 9.

Learning dynamics, which describes how the learning of specific training examples influences the model's predictions on other examples, gives us a powerful tool for understanding the behavior of deep learning systems. We study the learning dynamics of large language models during different types of finetuning, by analyzing the step-wise decomposition of how influence accumulates among different potential responses. Our framework allows a uniform interpretation of many interesting observations about the training of popular algorithms for both instruction tuning and preference tuning. In particular, we propose a hypothetical explanation of why specific types of hallucination are strengthened after finetuning, e.g., the model might use phrases or facts in the response for question B to answer question A, or the model might keep repeating similar simple phrases when generating responses. We also extend our framework and highlight a unique "squeezing effect" to explain a previously observed phenomenon in off-policy direct preference optimization (DPO), where running DPO for too long makes even the desired outputs less likely. This framework also provides insights into where the benefits of on-policy DPO and other variants come from. The analysis not only provides a novel perspective of understanding LLM's finetuning but also inspires a simple, effective method to improve alignment performance.

The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total value of the admitted items. Although optimal competitive algorithms are known for this problem, they may be fundamentally unfair, i.e., individual items may be treated inequitably in different ways. We formalize a practically-relevant notion of time fairness which effectively models a trade off between static and dynamic pricing in a motivating application such as cloud resource allocation, and show that existing algorithms perform poorly under this metric. We propose a parameterized deterministic algorithm where the parameter precisely captures the Pareto-optimal trade-off between fairness (static pricing) and competitiveness (dynamic pricing). We show that randomization is theoretically powerful enough to be simultaneously competitive and fair; however, it does not work well in experiments. To further improve the trade-off between fairness and competitiveness, we develop a nearly-optimal learning-augmented algorithm which is fair, consistent, and robust (competitive), showing substantial performance improvements in numerical experiments.

To optimally coordinate with others in cooperative games, it is often crucial to have information about one's collaborators: successful driving requires understanding which side of the road to drive on. However, not every feature of collaborators is strategically relevant: the fine-grained acceleration of drivers may be ignored while maintaining optimal coordination. We show that there is a well-defined dichotomy between strategically relevant and irrelevant information. Moreover, we show that, in dynamic games, this dichotomy has a compact representation that can be efficiently computed via a Bellman backup operator. We apply this algorithm to analyze the strategically relevant information for tasks in both a standard and a partially observable version of the Overcooked environment. Theoretical and empirical results show that our algorithms are significantly more efficient than baselines. Videos are available at https://minknowledge.github.io.

When one agent interacts with a multi-agent environment, it is challenging to deal with various opponents unseen before. Modeling the behaviors, goals, or beliefs of opponents could help the agent adjust its policy to adapt to different opponents. In addition, it is also important to consider opponents who are learning simultaneously or capable of reasoning. However, existing work usually tackles only one of the aforementioned types of opponents. In this paper, we propose model-based opponent modeling (MBOM), which employs the environment model to adapt to all kinds of opponents. MBOM simulates the recursive reasoning process in the environment model and imagines a set of improving opponent policies. To effectively and accurately represent the opponent policy, MBOM further mixes the imagined opponent policies according to the similarity with the real behaviors of opponents. Empirically, we show that MBOM achieves more effective adaptation than existing methods in a variety of tasks, respectively with different types of opponents, i.e., fixed policy, na\"ive learner, and reasoning learner.

This paper introduces Alympics (Olympics for Agents), a systematic simulation framework utilizing Large Language Model (LLM) agents for game theory research. Alympics creates a versatile platform for studying complex game theory problems, bridging the gap between theoretical game theory and empirical investigations by providing a controlled environment for simulating human-like strategic interactions with LLM agents. In our pilot case study, the "Water Allocation Challenge," we explore Alympics through a challenging strategic game focused on the multi-round auction on scarce survival resources. This study demonstrates the framework's ability to qualitatively and quantitatively analyze game determinants, strategies, and outcomes. Additionally, we conduct a comprehensive human assessment and an in-depth evaluation of LLM agents in strategic decision-making scenarios. Our findings not only expand the understanding of LLM agents' proficiency in emulating human strategic behavior but also highlight their potential in advancing game theory knowledge, thereby enriching our understanding of both game theory and empowering further research into strategic decision-making domains with LLM agents. Codes, prompts, and all related resources are available at https://github.com/microsoft/Alympics.

Recent advances in reinforcement learning (RL) heavily rely on a variety of well-designed benchmarks, which provide environmental platforms and consistent criteria to evaluate existing and novel algorithms. Specifically, in multi-agent RL (MARL), a plethora of benchmarks based on cooperative games have spurred the development of algorithms that improve the scalability of cooperative multi-agent systems. However, for the competitive setting, a lightweight and open-sourced benchmark with challenging gaming dynamics and visual inputs has not yet been established. In this work, we present FightLadder, a real-time fighting game platform, to empower competitive MARL research. Along with the platform, we provide implementations of state-of-the-art MARL algorithms for competitive games, as well as a set of evaluation metrics to characterize the performance and exploitability of agents. We demonstrate the feasibility of this platform by training a general agent that consistently defeats 12 built-in characters in single-player mode, and expose the difficulty of training a non-exploitable agent without human knowledge and demonstrations in two-player mode. FightLadder provides meticulously designed environments to address critical challenges in competitive MARL research, aiming to catalyze a new era of discovery and advancement in the field. Videos and code at https://sites.google.com/view/fightladder/home.

We initiate the study of Multi-Agent Reinforcement Learning from Human Feedback (MARLHF), exploring both theoretical foundations and empirical validations. We define the task as identifying Nash equilibrium from a preference-only offline dataset in general-sum games, a problem marked by the challenge of sparse feedback signals. Our theory establishes the upper complexity bounds for Nash Equilibrium in effective MARLHF, demonstrating that single-policy coverage is inadequate and highlighting the importance of unilateral dataset coverage. These theoretical insights are verified through comprehensive experiments. To enhance the practical performance, we further introduce two algorithmic techniques. (1) We propose a Mean Squared Error (MSE) regularization along the time axis to achieve a more uniform reward distribution and improve reward learning outcomes. (2) We utilize imitation learning to approximate the reference policy, ensuring stability and effectiveness in training. Our findings underscore the multifaceted approach required for MARLHF, paving the way for effective preference-based multi-agent systems.

The emergence and impact of tipping points have garnered significant interest in both the social and natural sciences. Despite widespread recognition of the importance of feedbacks between human and natural systems, it is often assumed that the observed nonlinear dynamics in these coupled systems rests within either underlying human or natural processes, rather than the rates at which they interact. Using adoption of agricultural diversification practices as a case study, we show how two stable management paradigms (one dominated by conventional, homogeneous practices, the other by diversified practices) can emerge purely from temporal feedbacks between human decisions and ecological responses. We explore how this temporal mechanism of tipping points provides insight into designing more effective interventions that promote farmers transitions towards sustainable agriculture. Moreover, our flexible modeling framework could be applied to other cases to provide insight into numerous questions in social-ecological systems research and environmental policy.

Information is often stored in a distributed and proprietary form, and agents who own information are often self-interested and require incentives to reveal their information. Suitable mechanisms are required to elicit and aggregate such distributed information for decision making. In this paper, we use simulations to investigate the use of decision markets as mechanisms in a multi-agent learning system to aggregate distributed information for decision-making in a contextual bandit problem. The system utilises strictly proper decision scoring rules to assess the accuracy of probabilistic reports from agents, which allows agents to learn to solve the contextual bandit problem jointly. Our simulations show that our multi-agent system with distributed information can be trained as efficiently as a centralised counterpart with a single agent that receives all information. Moreover, we use our system to investigate scenarios with deterministic decision scoring rules which are not incentive compatible. We observe the emergence of more complex dynamics with manipulative behaviour, which agrees with existing theoretical analyses.

Competitive Pok\'emon Singles (CPS) is a popular strategy game where players learn to exploit their opponent based on imperfect information in battles that can last more than one hundred stochastic turns. AI research in CPS has been led by heuristic tree search and online self-play, but the game may also create a platform to study adaptive policies trained offline on large datasets. We develop a pipeline to reconstruct the first-person perspective of an agent from logs saved from the third-person perspective of a spectator, thereby unlocking a dataset of real human battles spanning more than a decade that grows larger every day. This dataset enables a black-box approach where we train large sequence models to adapt to their opponent based solely on their input trajectory while selecting moves without explicit search of any kind. We study a progression from imitation learning to offline RL and offline fine-tuning on self-play data in the hardcore competitive setting of Pok\'emon's four oldest (and most partially observed) game generations. The resulting agents outperform a recent LLM Agent approach and a strong heuristic search engine. While playing anonymously in online battles against humans, our best agents climb to rankings inside the top 10% of active players.

The study of social emergence has long been a central focus in social science. Traditional modeling approaches, such as rule-based Agent-Based Models (ABMs), struggle to capture the diversity and complexity of human behavior, particularly the irrational factors emphasized in behavioral economics. Recently, large language model (LLM) agents have gained traction as simulation tools for modeling human behavior in social science and role-playing applications. Studies suggest that LLMs can account for cognitive biases, emotional fluctuations, and other non-rational influences, enabling more realistic simulations of socio-economic dynamics. In this work, we introduce TwinMarket, a novel multi-agent framework that leverages LLMs to simulate socio-economic systems. Specifically, we examine how individual behaviors, through interactions and feedback mechanisms, give rise to collective dynamics and emergent phenomena. Through experiments in a simulated stock market environment, we demonstrate how individual actions can trigger group behaviors, leading to emergent outcomes such as financial bubbles and recessions. Our approach provides valuable insights into the complex interplay between individual decision-making and collective socio-economic patterns.

Organizations typically train large models individually. This is costly and time-consuming, particularly for large-scale foundation models. Such vertical production is known to be suboptimal. Inspired by this economic insight, we ask whether it is possible to leverage others' expertise by trading the constituent parts in models, i.e., sets of weights, as if they were market commodities. While recent advances in aligning and interpolating models suggest that doing so may be possible, a number of fundamental questions must be answered to create viable parameter markets. In this work, we address these basic questions, propose a framework containing the infrastructure necessary for market operations to take place, study strategies for exchanging parameters, and offer means for agents to monetize parameters. Excitingly, compared to agents who train siloed models from scratch, we show that it is possible to mutually gain by using the market, even in competitive settings. This suggests that the notion of parameter markets may be a useful paradigm for improving large-scale model training in the future.

In financial trading, large language model (LLM)-based agents demonstrate significant potential. However, the high sensitivity to market noise undermines the performance of LLM-based trading systems. To address this limitation, we propose a novel multi-agent system featuring an internal competitive mechanism inspired by modern corporate management structures. The system consists of two specialized teams: (1) Data Team - responsible for processing and condensing massive market data into diversified text factors, ensuring they fit the model's constrained context. (2) Research Team - tasked with making parallelized multipath trading decisions based on deep research methods. The core innovation lies in implementing a real-time evaluation and ranking mechanism within each team, driven by authentic market feedback. Each agent's performance undergoes continuous scoring and ranking, with only outputs from top-performing agents being adopted. The design enables the system to adaptively adjust to dynamic environment, enhances robustness against market noise and ultimately delivers superior trading performance. Experimental results demonstrate that our proposed system significantly outperforms prevailing multi-agent systems and traditional quantitative investment methods across diverse evaluation metrics. ContestTrade is open-sourced on GitHub at https://github.com/FinStep-AI/ContestTrade.

We present a new type of game, the Liquidity Game. We draw inspiration from the UK government bond market and apply game theoretic approaches to its analysis. In Liquidity Games, market participants (agents) use non-cooperative games where the players' utility is directly defined by the liquidity of the game itself, offering a paradigm shift in our understanding of market dynamics. Each player's utility is intricately linked to the liquidity generated within the game, making the utility endogenous and dynamic. Players are not just passive recipients of utility based on external factors but active participants whose strategies and actions collectively shape and are shaped by the liquidity of the market. This reflexivity introduces a level of complexity and realism previously unattainable in conventional models. We apply Liquidity Game theoretic approaches to a simple UK bond market interaction and present results for market design and strategic behavior of participants. We tackle one of the largest issues within this mechanism, namely what strategy should market makers utilize when uncertain about the type of market maker they are interacting with, and what structure might regulators wish to see.

In online ad markets, a rising number of advertisers are employing bidding agencies to participate in ad auctions. These agencies are specialized in designing online algorithms and bidding on behalf of their clients. Typically, an agency usually has information on multiple advertisers, so she can potentially coordinate bids to help her clients achieve higher utilities than those under independent bidding. In this paper, we study coordinated online bidding algorithms in repeated second-price auctions with budgets. We propose algorithms that guarantee every client a higher utility than the best she can get under independent bidding. We show that these algorithms achieve maximal coalition welfare and discuss bidders' incentives to misreport their budgets, in symmetric cases. Our proofs combine the techniques of online learning and equilibrium analysis, overcoming the difficulty of competing with a multi-dimensional benchmark. The performance of our algorithms is further evaluated by experiments on both synthetic and real data. To the best of our knowledge, we are the first to consider bidder coordination in online repeated auctions with constraints.

A successful tactic that is followed by the scientific community for advancing AI is to treat games as problems, which has been proven to lead to various breakthroughs. We adapt this strategy in order to study Rocket League, a widely popular but rather under-explored 3D multiplayer video game with a distinct physics engine and complex dynamics that pose a significant challenge in developing efficient and high-performance game-playing agents. In this paper, we present Lucy-SKG, a Reinforcement Learning-based model that learned how to play Rocket League in a sample-efficient manner, outperforming by a notable margin the two highest-ranking bots in this game, namely Necto (2022 bot champion) and its successor Nexto, thus becoming a state-of-the-art agent. Our contributions include: a) the development of a reward analysis and visualization library, b) novel parameterizable reward shape functions that capture the utility of complex reward types via our proposed Kinesthetic Reward Combination (KRC) technique, and c) design of auxiliary neural architectures for training on reward prediction and state representation tasks in an on-policy fashion for enhanced efficiency in learning speed and performance. By performing thorough ablation studies for each component of Lucy-SKG, we showed their independent effectiveness in overall performance. In doing so, we demonstrate the prospects and challenges of using sample-efficient Reinforcement Learning techniques for controlling complex dynamical systems under competitive team-based multiplayer conditions.

We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO ), a gradient-based method that incorporates the interactions between the two players in zero-sum games for optimization updates. We provide continuous-time analysis of CGO and its convergence properties while showing that in the continuous limit, CGO predecessors degenerate to their gradient descent ascent (GDA) variants. We provide a rate of convergence to stationary points and further propose a generalized class of alpha-coherent function for which we provide convergence analysis. We show that for strictly alpha-coherent functions, our algorithm convergences to a saddle point. Moreover, we propose optimistic CGO (OCGO), an optimistic variant, for which we show convergence rate to saddle points in alpha-coherent class of functions.

Advancing towards generalist agents necessitates the concurrent processing of multiple tasks using a unified model, thereby underscoring the growing significance of simultaneous model training on multiple downstream tasks. A common issue in multi-task learning is the occurrence of gradient conflict, which leads to potential competition among different tasks during joint training. This competition often results in improvements in one task at the expense of deterioration in another. Although several optimization methods have been developed to address this issue by manipulating task gradients for better task balancing, they cannot decrease the incidence of gradient conflict. In this paper, we systematically investigate the occurrence of gradient conflict across different methods and propose a strategy to reduce such conflicts through sparse training (ST), wherein only a portion of the model's parameters are updated during training while keeping the rest unchanged. Our extensive experiments demonstrate that ST effectively mitigates conflicting gradients and leads to superior performance. Furthermore, ST can be easily integrated with gradient manipulation techniques, thus enhancing their effectiveness.

Many examples of cooperation exist in biology. In chemical systems however, which can sometimes be quite complex, we do not appear to observe intricate cooperative interactions. A key question for the origin of life, is then how can molecular cooperation first arise in an abiotic system prior to the emergence of biological replication. We postulate that selection at the molecular level is a driving force behind the complexification of chemical systems, particularly during the origins of life. In the theory of multilevel selection the two selective forces are: within-group and between-group, where the former tends to favor "selfish" replication of individuals and the latter favor cooperation between individuals enhancing the replication of the group as a whole. These forces can be quantified using the Price equation, which is a standard tool used in evolutionary biology to quantify evolutionary change. Our central claim is that replication and heredity in chemical systems are subject to selection, and quantifiable using the multilevel Price equation. We demonstrate this using the Graded Autocatalysis Replication Domain computer model, describing simple protocell composed out of molecules and its replication, which respectively analogue to the group and the individuals. In contrast to previous treatments of this model, we treat the lipid molecules themselves as replicating individuals and the protocells they form as groups of individuals. Our goal is to demonstrate how evolutionary biology tools and concepts can be applied in chemistry and we suggest that molecular cooperation may arise as a result of group selection. Further, the biological relation of parent-progeny is proposed to be analogue to the reactant-product relation in chemistry, thus allowing for tools from evolutionary biology to be applied to chemistry and would deepen the connection between chemistry and biology.

Congestion is a common failure mode of markets, where consumers compete inefficiently on the same subset of goods (e.g., chasing the same small set of properties on a vacation rental platform). The typical economic story is that prices decongest by balancing supply and demand. But in modern online marketplaces, prices are typically set in a decentralized way by sellers, and the information about items is inevitably partial. The power of a platform is limited to controlling representations -- the subset of information about items presented by default to users. This motivates the present study of decongestion by representation, where a platform seeks to learn representations that reduce congestion and thus improve social welfare. The technical challenge is twofold: relying only on revealed preferences from the choices of consumers, rather than true preferences; and the combinatorial problem associated with representations that determine the features to reveal in the default view. We tackle both challenges by proposing a differentiable proxy of welfare that can be trained end-to-end on consumer choice data. We develop sufficient conditions for when decongestion promotes welfare, and present the results of extensive experiments on both synthetic and real data that demonstrate the utility of our approach.

In this paper, we present a conceptual model game to examine the dynamics of asymmetric interactions in games with imperfect information. The game involves two agents with starkly contrasting capabilities: one agent can take actions but has no information of the state of the game, whereas the other agent has perfect information of the state but cannot act or observe the other agent's actions. This duality manifests an extreme form of asymmetry, and how differing abilities influence the possibility of attaining common knowledge. Using Kripke structures and epistemic logic we demonstrate that, under these conditions, common knowledge of the current game state becomes unattainable. Our findings advance the discussion on the strategic limitations of knowledge in environments where information and action are unevenly distributed.

Optimizing user engagement is a key goal for modern recommendation systems, but blindly pushing users towards increased consumption risks burn-out, churn, or even addictive habits. To promote digital well-being, most platforms now offer a service that periodically prompts users to take breaks. These, however, must be set up manually, and so may be suboptimal for both users and the system. In this paper, we study the role of breaks in recommendation, and propose a framework for learning optimal breaking policies that promote and sustain long-term engagement. Based on the notion that recommendation dynamics are susceptible to both positive and negative feedback, we cast recommendation as a Lotka-Volterra dynamical system, where breaking reduces to a problem of optimal control. We then give an efficient learning algorithm, provide theoretical guarantees, and empirically demonstrate the utility of our approach on semi-synthetic data.

Solving the problem of cooperation is fundamentally important for the creation and maintenance of functional societies. Problems of cooperation are omnipresent within human society, with examples ranging from navigating busy road junctions to negotiating treaties. As the use of AI becomes more pervasive throughout society, the need for socially intelligent agents capable of navigating these complex cooperative dilemmas is becoming increasingly evident. Direct punishment is a ubiquitous social mechanism that has been shown to foster the emergence of cooperation in both humans and non-humans. In the natural world, direct punishment is often strongly coupled with partner selection and reputation and used in conjunction with third-party punishment. The interactions between these mechanisms could potentially enhance the emergence of cooperation within populations. However, no previous work has evaluated the learning dynamics and outcomes emerging from Multi-Agent Reinforcement Learning (MARL) populations that combine these mechanisms. This paper addresses this gap. It presents a comprehensive analysis and evaluation of the behaviors and learning dynamics associated with direct punishment, third-party punishment, partner selection, and reputation. Finally, we discuss the implications of using these mechanisms on the design of cooperative AI systems.

Generative language models are increasingly used for contract drafting and enhancement, creating a scenario where competing parties deploy different language models against each other. This introduces not only a game-theory challenge but also significant concerns related to AI safety and security, as the language model employed by the opposing party can be unknown. These competitive interactions can be seen as adversarial testing grounds, where models are effectively red-teamed to expose vulnerabilities such as generating biased, harmful or legally problematic text. Despite the importance of these challenges, the competitive robustness and safety of these models in adversarial settings remain poorly understood. In this small study, we approach this problem by evaluating the performance and vulnerabilities of major open-source language models in head-to-head competitions, simulating real-world contract negotiations. We further explore how these adversarial interactions can reveal potential risks, informing the development of more secure and reliable models. Our findings contribute to the growing body of research on AI safety, offering insights into model selection and optimisation in competitive legal contexts and providing actionable strategies for mitigating risks.

We investigated the temporal distribution of goals in soccer using event-level data from 3,433 matches across 21 leagues and competitions. Contrary to the prevailing notion of randomness, we found that the probability of a goal being scored is higher as matches progress, and we observed fewer-than-expected goals in the early minutes of each half. Further analysis of the time between subsequent goals shows an exponential decay, indicating that most goals naturally cluster closer together in time. By splitting this distribution by the team that scores the next goal, we observe bursty goal-scoring dynamics, wherein the same team is more likely to score again shortly after its previous goal. These findings highlight the importance of match context (whether driven by fatigue, tactical adaptations, or psychological momentum) in shaping when teams are able to score. Moreover, the results open avenues for extending data-driven methods for identifying high-impact moments in a match and refining strategic decision-making in soccer's evolving analytical landscape.

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02\% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.

Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service delivery times and gauge the service quality based on the service provider's ability to complete the service as close as possible to the preferred time. Customers can be of different priority classes, and their priority may increase as they wait longer in the queue. The service provider can reject customers upon their arrival if the system is overloaded or outsource the service (alternatively work overtime) when the capacity is not enough. The service provider's goal is to find the minimum-cost admission and capacity allocation policy to dynamically decide when to serve and whom to serve. We model this problem as a Markov Decision Process. Our structural results partially characterize a set of suboptimal solutions, and we develop solution methods using these results. We also develop a problem-specific approximation method that is based on state aggregation to overcome the computational challenges. We present extensive computational results and discuss the impact of problem parameters on the optimal policy.

Governments are increasingly considering integrating autonomous AI agents in high-stakes military and foreign-policy decision-making, especially with the emergence of advanced generative AI models like GPT-4. Our work aims to scrutinize the behavior of multiple AI agents in simulated wargames, specifically focusing on their predilection to take escalatory actions that may exacerbate multilateral conflicts. Drawing on political science and international relations literature about escalation dynamics, we design a novel wargame simulation and scoring framework to assess the escalation risks of actions taken by these agents in different scenarios. Contrary to prior studies, our research provides both qualitative and quantitative insights and focuses on large language models (LLMs). We find that all five studied off-the-shelf LLMs show forms of escalation and difficult-to-predict escalation patterns. We observe that models tend to develop arms-race dynamics, leading to greater conflict, and in rare cases, even to the deployment of nuclear weapons. Qualitatively, we also collect the models' reported reasonings for chosen actions and observe worrying justifications based on deterrence and first-strike tactics. Given the high stakes of military and foreign-policy contexts, we recommend further examination and cautious consideration before deploying autonomous language model agents for strategic military or diplomatic decision-making.

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.

We introduce an Implicit Game-Theoretic MPC (IGT-MPC), a decentralized algorithm for two-agent motion planning that uses a learned value function that predicts the game-theoretic interaction outcomes as the terminal cost-to-go function in a model predictive control (MPC) framework, guiding agents to implicitly account for interactions with other agents and maximize their reward. This approach applies to competitive and cooperative multi-agent motion planning problems which we formulate as constrained dynamic games. Given a constrained dynamic game, we randomly sample initial conditions and solve for the generalized Nash equilibrium (GNE) to generate a dataset of GNE solutions, computing the reward outcome of each game-theoretic interaction from the GNE. The data is used to train a simple neural network to predict the reward outcome, which we use as the terminal cost-to-go function in an MPC scheme. We showcase emerging competitive and coordinated behaviors using IGT-MPC in scenarios such as two-vehicle head-to-head racing and un-signalized intersection navigation. IGT-MPC offers a novel method integrating machine learning and game-theoretic reasoning into model-based decentralized multi-agent motion planning.

End-to-end autonomous driving models trained solely with imitation learning (IL) often suffer from poor generalization. In contrast, reinforcement learning (RL) promotes exploration through reward maximization but faces challenges such as sample inefficiency and unstable convergence. A natural solution is to combine IL and RL. Moving beyond the conventional two-stage paradigm (IL pretraining followed by RL fine-tuning), we propose CoIRL-AD, a competitive dual-policy framework that enables IL and RL agents to interact during training. CoIRL-AD introduces a competition-based mechanism that facilitates knowledge exchange while preventing gradient conflicts. Experiments on the nuScenes dataset show an 18% reduction in collision rate compared to baselines, along with stronger generalization and improved performance on long-tail scenarios. Code is available at: https://github.com/SEU-zxj/CoIRL-AD.

Motivated by equilibrium models of labor markets, we develop a formulation of causal strategic classification in which strategic agents can directly manipulate their outcomes. As an application, we compare employers that anticipate the strategic response of a labor force with employers that do not. We show through a combination of theory and experiment that employers with performatively optimal hiring policies improve employer reward, labor force skill level, and in some cases labor force equity. On the other hand, we demonstrate that performative employers harm labor force utility and fail to prevent discrimination in other cases.

The computational study of equilibria involving constraints on players' strategies has been largely neglected. However, in real-world applications, players are usually subject to constraints ruling out the feasibility of some of their strategies, such as, e.g., safety requirements and budget caps. Computational studies on constrained versions of the Nash equilibrium have lead to some results under very stringent assumptions, while finding constrained versions of the correlated equilibrium (CE) is still unexplored. In this paper, we introduce and computationally characterize constrained Phi-equilibria -- a more general notion than constrained CEs -- in normal-form games. We show that computing such equilibria is in general computationally intractable, and also that the set of the equilibria may not be convex, providing a sharp divide with unconstrained CEs. Nevertheless, we provide a polynomial-time algorithm for computing a constrained (approximate) Phi-equilibrium maximizing a given linear function, when either the number of constraints or that of players' actions is fixed. Moreover, in the special case in which a player's constraints do not depend on other players' strategies, we show that an exact, function-maximizing equilibrium can be computed in polynomial time, while one (approximate) equilibrium can be found with an efficient decentralized no-regret learning algorithm.

Critical learning periods are periods early in development where temporary sensory deficits can have a permanent effect on behavior and learned representations. Despite the radical differences between biological and artificial networks, critical learning periods have been empirically observed in both systems. This suggests that critical periods may be fundamental to learning and not an accident of biology. Yet, why exactly critical periods emerge in deep networks is still an open question, and in particular it is unclear whether the critical periods observed in both systems depend on particular architectural or optimization details. To isolate the key underlying factors, we focus on deep linear network models, and show that, surprisingly, such networks also display much of the behavior seen in biology and artificial networks, while being amenable to analytical treatment. We show that critical periods depend on the depth of the model and structure of the data distribution. We also show analytically and in simulations that the learning of features is tied to competition between sources. Finally, we extend our analysis to multi-task learning to show that pre-training on certain tasks can damage the transfer performance on new tasks, and show how this depends on the relationship between tasks and the duration of the pre-training stage. To the best of our knowledge, our work provides the first analytically tractable model that sheds light into why critical learning periods emerge in biological and artificial networks.

In democracies, major policy decisions typically require some form of majority or consensus, so elites must secure mass support to govern. Historically, elites could shape support only through limited instruments like schooling and mass media; advances in AI-driven persuasion sharply reduce the cost and increase the precision of shaping public opinion, making the distribution of preferences itself an object of deliberate design. We develop a dynamic model in which elites choose how much to reshape the distribution of policy preferences, subject to persuasion costs and a majority rule constraint. With a single elite, any optimal intervention tends to push society toward more polarized opinion profiles - a ``polarization pull'' - and improvements in persuasion technology accelerate this drift. When two opposed elites alternate in power, the same technology also creates incentives to park society in ``semi-lock'' regions where opinions are more cohesive and harder for a rival to overturn, so advances in persuasion can either heighten or dampen polarization depending on the environment. Taken together, cheaper persuasion technologies recast polarization as a strategic instrument of governance rather than a purely emergent social byproduct, with important implications for democratic stability as AI capabilities advance.

Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This paper introduces a market microstructure framework that models matching decisions as a limit order book system with rigid bid ask spreads. Individual preferences are represented by a latent preference state matrix, where the spread between an agent's internal ask price (the unconditional maximum) and the market's best bid (the reachable maximum) creates a structural liquidity constraint. We establish a Threshold Impossibility Theorem showing that linear compensation cannot close these spreads unless it induces a categorical identity shift. A dynamic discrete choice execution model further demonstrates that matches occur only when the market to book ratio crosses a time decaying liquidity threshold, analogous to order execution under inventory pressure. Numerical experiments validate persistent slippage, regional invariance of preference orderings, and high tier zero spread executions. The model provides a unified microstructure explanation for matching failures, compensation inefficiency, and post match regret in illiquid order driven environments.

Price responsiveness is a major feature of end use customers (EUCs) that participate in demand response (DR) programs, and has been conventionally modeled with static demand functions, which take the electricity price as the input and the aggregate energy consumption as the output. This, however, neglects the inherent temporal correlation of the EUC behaviors, and may result in large errors when predicting the actual responses of EUCs in real-time pricing (RTP) programs. In this paper, we propose a dynamical DR model so as to capture the temporal behavior of the EUCs. The states in the proposed dynamical DR model can be explicitly chosen, in which case the model can be represented by a linear function or a multi-layer feedforward neural network, or implicitly chosen, in which case the model can be represented by a recurrent neural network or a long short-term memory unit network. In both cases, the dynamical DR model can be learned from historical price and energy consumption data. Numerical simulation illustrated how the states are chosen and also showed the proposed dynamical DR model significantly outperforms the static ones.

This survey draws a broad-stroke, panoramic picture of the State of the Art (SoTA) of the research in generative methods for the analysis of social media data. It fills a void, as the existing survey articles are either much narrower in their scope or are dated. We included two important aspects that currently gain importance in mining and modeling social media: dynamics and networks. Social dynamics are important for understanding the spreading of influence or diseases, formation of friendships, the productivity of teams, etc. Networks, on the other hand, may capture various complex relationships providing additional insight and identifying important patterns that would otherwise go unnoticed.

We study an online learning problem in general-sum Stackelberg games, where players act in a decentralized and strategic manner. We study two settings depending on the type of information for the follower: (1) the limited information setting where the follower only observes its own reward, and (2) the side information setting where the follower has extra side information about the leader's reward. We show that for the follower, myopically best responding to the leader's action is the best strategy for the limited information setting, but not necessarily so for the side information setting -- the follower can manipulate the leader's reward signals with strategic actions, and hence induce the leader's strategy to converge to an equilibrium that is better off for itself. Based on these insights, we study decentralized online learning for both players in the two settings. Our main contribution is to derive last-iterate convergence and sample complexity results in both settings. Notably, we design a new manipulation strategy for the follower in the latter setting, and show that it has an intrinsic advantage against the best response strategy. Our theories are also supported by empirical results.

For the immanent challenge of insufficiently annotated samples in the medical field, semi-supervised medical image segmentation (SSMIS) offers a promising solution. Despite achieving impressive results in delineating primary target areas, most current methodologies struggle to precisely capture the subtle details of boundaries. This deficiency often leads to significant diagnostic inaccuracies. To tackle this issue, we introduce C3S3, a novel semi-supervised segmentation model that synergistically integrates complementary competition and contrastive selection. This design significantly sharpens boundary delineation and enhances overall precision. Specifically, we develop an Outcome-Driven Contrastive Learning module dedicated to refining boundary localization. Additionally, we incorporate a Dynamic Complementary Competition module that leverages two high-performing sub-networks to generate pseudo-labels, thereby further improving segmentation quality. The proposed C3S3 undergoes rigorous validation on two publicly accessible datasets, encompassing the practices of both MRI and CT scans. The results demonstrate that our method achieves superior performance compared to previous cutting-edge competitors. Especially, on the 95HD and ASD metrics, our approach achieves a notable improvement of at least 6%, highlighting the significant advancements. The code is available at https://github.com/Y-TARL/C3S3.

In various real-world scenarios, interactions among agents often resemble the dynamics of general-sum games, where each agent strives to optimize its own utility. Despite the ubiquitous relevance of such settings, decentralized machine learning algorithms have struggled to find equilibria that maximize individual utility while preserving social welfare. In this paper we introduce Learning with Opponent Q-Learning Awareness (LOQA), a novel, decentralized reinforcement learning algorithm tailored to optimizing an agent's individual utility while fostering cooperation among adversaries in partially competitive environments. LOQA assumes the opponent samples actions proportionally to their action-value function Q. Experimental results demonstrate the effectiveness of LOQA at achieving state-of-the-art performance in benchmark scenarios such as the Iterated Prisoner's Dilemma and the Coin Game. LOQA achieves these outcomes with a significantly reduced computational footprint, making it a promising approach for practical multi-agent applications.

Card games are widely used to study sequential decision-making under uncertainty, with real-world analogues in negotiation, finance, and cybersecurity. These games typically fall into three categories based on the flow of control: strictly sequential (players alternate single actions), deterministic response (some actions trigger a fixed outcome), and unbounded reciprocal response (alternating counterplays are permitted). A less-explored but strategically rich structure is the bounded one-sided response, where a player's action briefly transfers control to the opponent, who must satisfy a fixed condition through one or more moves before the turn resolves. We term games featuring this mechanism Bounded One-Sided Response Games (BORGs). We introduce a modified version of Monopoly Deal as a benchmark environment that isolates this dynamic, where a Rent action forces the opponent to choose payment assets. The gold-standard algorithm, Counterfactual Regret Minimization (CFR), converges on effective strategies without novel algorithmic extensions. A lightweight full-stack research platform unifies the environment, a parallelized CFR runtime, and a human-playable web interface. The trained CFR agent and source code are available at https://monopolydeal.ai.

Unsupervised reinforcement learning (RL) studies how to leverage environment statistics to learn useful behaviors without the cost of reward engineering. However, a central challenge in unsupervised RL is to extract behaviors that meaningfully affect the world and cover the range of possible outcomes, without getting distracted by inherently unpredictable, uncontrollable, and stochastic elements in the environment. To this end, we propose an unsupervised RL method designed for high-dimensional, stochastic environments based on an adversarial game between two policies (which we call Explore and Control) controlling a single body and competing over the amount of observation entropy the agent experiences. The Explore agent seeks out states that maximally surprise the Control agent, which in turn aims to minimize surprise, and thereby manipulate the environment to return to familiar and predictable states. The competition between these two policies drives them to seek out increasingly surprising parts of the environment while learning to gain mastery over them. We show formally that the resulting algorithm maximizes coverage of the underlying state in block MDPs with stochastic observations, providing theoretical backing to our hypothesis that this procedure avoids uncontrollable and stochastic distractions. Our experiments further demonstrate that Adversarial Surprise leads to the emergence of complex and meaningful skills, and outperforms state-of-the-art unsupervised reinforcement learning methods in terms of both exploration and zero-shot transfer to downstream tasks.

Evolvability is an important feature that impacts the ability of evolutionary processes to find interesting novel solutions and to deal with changing conditions of the problem to solve. The estimation of evolvability is not straightforward and is generally too expensive to be directly used as selective pressure in the evolutionary process. Indirectly promoting evolvability as a side effect of other easier and faster to compute selection pressures would thus be advantageous. In an unbounded behavior space, it has already been shown that evolvable individuals naturally appear and tend to be selected as they are more likely to invade empty behavior niches. Evolvability is thus a natural byproduct of the search in this context. However, practical agents and environments often impose limits on the reach-able behavior space. How do these boundaries impact evolvability? In this context, can evolvability still be promoted without explicitly rewarding it? We show that Novelty Search implicitly creates a pressure for high evolvability even in bounded behavior spaces, and explore the reasons for such a behavior. More precisely we show that, throughout the search, the dynamic evaluation of novelty rewards individuals which are very mobile in the behavior space, which in turn promotes evolvability.

This paper generalises the treatment of compositional game theory as introduced by the second and third authors with Ghani and Winschel, where games are modelled as morphisms of a symmetric monoidal category. From an economic modelling perspective, the existing notion of an open game is not expressive enough for many applications. This includes stochastic environments, stochastic choices by players, as well as incomplete information regarding the game being played. The current paper addresses these three issue all at once. To achieve this we make significant use of category theory, especially the 'coend optics' of Riley.

Multi-agent systems often require agents to collaborate with or compete against other agents with diverse goals, behaviors, or strategies. Agent modeling is essential when designing adaptive policies for intelligent machine agents in multiagent systems, as this is the means by which the ego agent understands other agents' behavior and extracts their meaningful policy representations. These representations can be used to enhance the ego agent's adaptive policy which is trained by reinforcement learning. However, existing agent modeling approaches typically assume the availability of local observations from other agents (modeled agents) during training or a long observation trajectory for policy adaption. To remove these constrictive assumptions and improve agent modeling performance, we devised a Contrastive Learning-based Agent Modeling (CLAM) method that relies only on the local observations from the ego agent during training and execution. With these observations, CLAM is capable of generating consistent high-quality policy representations in real-time right from the beginning of each episode. We evaluated the efficacy of our approach in both cooperative and competitive multi-agent environments. Our experiments demonstrate that our approach achieves state-of-the-art on both cooperative and competitive tasks, highlighting the potential of contrastive learning-based agent modeling for enhancing reinforcement learning.

Playing games has a long history of describing intricate interactions in simplified forms. In this paper we explore if large language models (LLMs) can play games, investigating their capabilities for randomisation and strategic adaptation through both simultaneous and sequential game interactions. We focus on GPT-4o-Mini-2024-08-17 and test two games between LLMs: Rock Paper Scissors (RPS) and games of strategy (Prisoners Dilemma PD). LLMs are often described as stochastic parrots, and while they may indeed be parrots, our results suggest that they are not very stochastic in the sense that their outputs - when prompted to be random - are often very biased. Our research reveals that LLMs appear to develop loss aversion strategies in repeated games, with RPS converging to stalemate conditions while PD shows systematic shifts between cooperative and competitive outcomes based on prompt design. We detail programmatic tools for independent agent interactions and the Agentic AI challenges faced in implementation. We show that LLMs can indeed play games, just not very well. These results have implications for the use of LLMs in multi-agent LLM systems and showcase limitations in current approaches to model output for strategic decision-making.

While the field of multi-modal learning keeps growing fast, the deficiency of the standard joint training paradigm has become clear through recent studies. They attribute the sub-optimal performance of the jointly trained model to the modality competition phenomenon. Existing works attempt to improve the jointly trained model by modulating the training process. Despite their effectiveness, those methods can only apply to late fusion models. More importantly, the mechanism of the modality competition remains unexplored. In this paper, we first propose an adaptive gradient modulation method that can boost the performance of multi-modal models with various fusion strategies. Extensive experiments show that our method surpasses all existing modulation methods. Furthermore, to have a quantitative understanding of the modality competition and the mechanism behind the effectiveness of our modulation method, we introduce a novel metric to measure the competition strength. This metric is built on the mono-modal concept, a function that is designed to represent the competition-less state of a modality. Through systematic investigation, our results confirm the intuition that the modulation encourages the model to rely on the more informative modality. In addition, we find that the jointly trained model typically has a preferred modality on which the competition is weaker than other modalities. However, this preferred modality need not dominate others. Our code will be available at https://github.com/lihong2303/AGM_ICCV2023.

Retrieval-Augmented Generation (RAG) systems, widely used to improve the factual grounding of large language models (LLMs), are increasingly vulnerable to poisoning attacks, where adversaries inject manipulated content into the retriever's corpus. While prior research has predominantly focused on single-attacker settings, real-world scenarios often involve multiple, competing attackers with conflicting objectives. In this work, we introduce PoisonArena, the first benchmark to systematically study and evaluate competing poisoning attacks in RAG. We formalize the multi-attacker threat model, where attackers vie to control the answer to the same query using mutually exclusive misinformation. PoisonArena leverages the Bradley-Terry model to quantify each method's competitive effectiveness in such adversarial environments. Through extensive experiments on the Natural Questions and MS MARCO datasets, we demonstrate that many attack strategies successful in isolation fail under competitive pressure. Our findings highlight the limitations of conventional evaluation metrics like Attack Success Rate (ASR) and F1 score and underscore the need for competitive evaluation to assess real-world attack robustness. PoisonArena provides a standardized framework to benchmark and develop future attack and defense strategies under more realistic, multi-adversary conditions.

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across novel samples and unseen environments. Flow-based models allow for learning these dynamics at the population level - they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We argue that multiple processes in natural sciences have to be represented as vector fields on the Wasserstein manifold of probability densities. That is, the change of the population at any moment in time depends on the population itself due to the interactions between samples. In particular, this is crucial for personalized medicine where the development of diseases and their respective treatment response depends on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrating along these vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. Namely, we embed the population of samples using a Graph Neural Network (GNN) and use these embeddings to train a Flow Matching model. This gives MFM the ability to generalize over the initial distributions unlike previously proposed methods. We demonstrate the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.

Equipping agents with the capacity to justify made decisions using supporting evidence represents a cornerstone of accountable decision-making. Furthermore, ensuring that justifications are in line with human expectations and societal norms is vital, especially in high-stakes situations such as healthcare. In this work, we propose the use of a debate-based reward model for reinforcement learning agents, where the outcome of a zero-sum debate game quantifies the justifiability of a decision in a particular state. This reward model is then used to train a justifiable policy, whose decisions can be more easily corroborated with supporting evidence. In the debate game, two argumentative agents take turns providing supporting evidence for two competing decisions. Given the proposed evidence, a proxy of a human judge evaluates which decision is better justified. We demonstrate the potential of our approach in learning policies for prescribing and justifying treatment decisions of septic patients. We show that augmenting the reward with the feedback signal generated by the debate-based reward model yields policies highly favored by the judge when compared to the policy obtained solely from the environment rewards, while hardly sacrificing any performance. Moreover, in terms of the overall performance and justifiability of trained policies, the debate-based feedback is comparable to the feedback obtained from an ideal judge proxy that evaluates decisions using the full information encoded in the state. This suggests that the debate game outputs key information contained in states that is most relevant for evaluating decisions, which in turn substantiates the practicality of combining our approach with human-in-the-loop evaluations. Lastly, we showcase that agents trained via multi-agent debate learn to propose evidence that is resilient to refutations and closely aligns with human preferences.

Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime called the "edge of stability." In this paper, we develop theory that can describe the dynamics of optimization in this regime. Our key insight is that while the *exact* trajectory of an oscillatory optimizer may be challenging to analyze, the *time-averaged* (i.e. smoothed) trajectory is often much more tractable. To analyze an optimizer, we derive a differential equation called a "central flow" that characterizes this time-averaged trajectory. We empirically show that these central flows can predict long-term optimization trajectories for generic neural networks with a high degree of numerical accuracy. By interpreting these central flows, we are able to understand how gradient descent makes progress even as the loss sometimes goes up; how adaptive optimizers "adapt" to the local loss landscape; and how adaptive optimizers implicitly navigate towards regions where they can take larger steps. Our results suggest that central flows can be a valuable theoretical tool for reasoning about optimization in deep learning.

Learning a precise dynamics model can be crucial for offline reinforcement learning, which, unfortunately, has been found to be quite challenging. Dynamics models that are learned by fitting historical transitions often struggle to generalize to unseen transitions. In this study, we identify a hidden but pivotal factor termed dynamics reward that remains consistent across transitions, offering a pathway to better generalization. Therefore, we propose the idea of reward-consistent dynamics models: any trajectory generated by the dynamics model should maximize the dynamics reward derived from the data. We implement this idea as the MOREC (Model-based Offline reinforcement learning with Reward Consistency) method, which can be seamlessly integrated into previous offline model-based reinforcement learning (MBRL) methods. MOREC learns a generalizable dynamics reward function from offline data, which is subsequently employed as a transition filter in any offline MBRL method: when generating transitions, the dynamics model generates a batch of transitions and selects the one with the highest dynamics reward value. On a synthetic task, we visualize that MOREC has a strong generalization ability and can surprisingly recover some distant unseen transitions. On 21 offline tasks in D4RL and NeoRL benchmarks, MOREC improves the previous state-of-the-art performance by a significant margin, i.e., 4.6% on D4RL tasks and 25.9% on NeoRL tasks. Notably, MOREC is the first method that can achieve above 95% online RL performance in 6 out of 12 D4RL tasks and 3 out of 9 NeoRL tasks.

We consider a biological population whose environment varies periodically in time, exhibiting two very different "seasons" : one is favorable and the other one is unfavorable. For monotone differential models with concave nonlinearities, we address the following question: the system's period being fixed, under what conditions does there exist a critical duration for the unfavorable season? By "critical duration" we mean that above some threshold, the population cannot sustain and extincts, while below this threshold, the system converges to a unique periodic and positive solution. We term this a "sharp seasonal threshold property" (SSTP, for short). Building upon a previous result, we obtain sufficient conditions for SSTP in any dimension and apply our criterion to a two-dimensional model featuring juvenile and adult populations of insects.

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

Reflecting the recent rise in Japanese basketball's competitiveness and pivotal outcomes in international tournaments, clutch-time performance has become increasingly critical. We examine clutch-time performance in Japan's B.League using play-by-play and box-score data from the 2023-24 season. Defining clutch time as the final five minutes with a score margin within five points, we compare efficiency and shot selection between clutch and non-clutch windows. We focus on effective field-goal percentage (eFG%) by spatial category, including In the Paint, Mid-Range, and 3-Point, and investigate league-wide and team-level trends. We further profile player archetypes in clutch minutes via K-means clustering on filtered box-score features. Results show that paint touches and clean three-point looks remain comparatively efficient under pressure, whereas mid-range outcomes are more context-dependent. Championship games exhibit tighter defense and scouting, moderating three-point accuracy for many teams. Our findings highlight the need for tactical flexibility, balancing efficient shot selection with adaptive counters to defensive pressure. We discuss strategic implications for late-game play-calling, spacing, and lineup choices, and outline limitations and future directions.

Investigating active learning, we focus on the relation between the number of labeled examples (budget size), and suitable querying strategies. Our theoretical analysis shows a behavior reminiscent of phase transition: typical examples are best queried when the budget is low, while unrepresentative examples are best queried when the budget is large. Combined evidence shows that a similar phenomenon occurs in common classification models. Accordingly, we propose TypiClust -- a deep active learning strategy suited for low budgets. In a comparative empirical investigation of supervised learning, using a variety of architectures and image datasets, TypiClust outperforms all other active learning strategies in the low-budget regime. Using TypiClust in the semi-supervised framework, performance gets an even more significant boost. In particular, state-of-the-art semi-supervised methods trained on CIFAR-10 with 10 labeled examples selected by TypiClust, reach 93.2% accuracy -- an improvement of 39.4% over random selection. Code is available at https://github.com/avihu111/TypiClust.

Budget management strategies in repeated auctions have received growing attention in online advertising markets. However, previous work on budget management in online bidding mainly focused on second-price auctions. The rapid shift from second-price auctions to first-price auctions for online ads in recent years has motivated the challenging question of how to bid in repeated first-price auctions while controlling budgets. In this work, we study the problem of learning in repeated first-price auctions with budgets. We design a dual-based algorithm that can achieve a near-optimal O(T) regret with full information feedback where the maximum competing bid is always revealed after each auction. We further consider the setting with one-sided information feedback where only the winning bid is revealed after each auction. We show that our modified algorithm can still achieve an O(T) regret with mild assumptions on the bidder's value distribution. Finally, we complement the theoretical results with numerical experiments to confirm the effectiveness of our budget management policy.

Probabilistic dynamics model ensemble is widely used in existing model-based reinforcement learning methods as it outperforms a single dynamics model in both asymptotic performance and sample efficiency. In this paper, we provide both practical and theoretical insights on the empirical success of the probabilistic dynamics model ensemble through the lens of Lipschitz continuity. We find that, for a value function, the stronger the Lipschitz condition is, the smaller the gap between the true dynamics- and learned dynamics-induced Bellman operators is, thus enabling the converged value function to be closer to the optimal value function. Hence, we hypothesize that the key functionality of the probabilistic dynamics model ensemble is to regularize the Lipschitz condition of the value function using generated samples. To test this hypothesis, we devise two practical robust training mechanisms through computing the adversarial noise and regularizing the value network's spectral norm to directly regularize the Lipschitz condition of the value functions. Empirical results show that combined with our mechanisms, model-based RL algorithms with a single dynamics model outperform those with an ensemble of probabilistic dynamics models. These findings not only support the theoretical insight, but also provide a practical solution for developing computationally efficient model-based RL algorithms.

The realm of High-Frequency Trading (HFT) is characterized by rapid decision-making processes that capitalize on fleeting market inefficiencies. As the financial markets become increasingly competitive, there is a pressing need for innovative strategies that can adapt and evolve with changing market dynamics. Enter Reinforcement Learning (RL), a branch of machine learning where agents learn by interacting with their environment, making it an intriguing candidate for HFT applications. This paper dives deep into the integration of RL in statistical arbitrage strategies tailored for HFT scenarios. By leveraging the adaptive learning capabilities of RL, we explore its potential to unearth patterns and devise trading strategies that traditional methods might overlook. We delve into the intricate exploration-exploitation trade-offs inherent in RL and how they manifest in the volatile world of HFT. Furthermore, we confront the challenges of applying RL in non-stationary environments, typical of financial markets, and investigate methodologies to mitigate associated risks. Through extensive simulations and backtests, our research reveals that RL not only enhances the adaptability of trading strategies but also shows promise in improving profitability metrics and risk-adjusted returns. This paper, therefore, positions RL as a pivotal tool for the next generation of HFT-based statistical arbitrage, offering insights for both researchers and practitioners in the field.

In this paper, we evaluate whether LLMs learn to make human-like preference judgements in strategic scenarios as compared with known empirical results. Solar and Mistral are shown to exhibit stable value-based preference consistent with humans and exhibit human-like preference for cooperation in the prisoner's dilemma (including stake-size effect) and traveler's dilemma (including penalty-size effect). We establish a relationship between model size, value-based preference, and superficiality. Finally, results here show that models tending to be less brittle have relied on sliding window attention suggesting a potential link. Additionally, we contribute a novel method for constructing preference relations from arbitrary LLMs and support for a hypothesis regarding human behavior in the traveler's dilemma.

This paper introduces a novel framework combining LLM agents as proxies for human strategic behavior with reinforcement learning (RL) to engage these agents in evolving strategic interactions within team environments. Our approach extends traditional agent-based simulations by using strategic LLM agents (SLA) and introducing dynamic and adaptive governance through a pro-social promoting RL agent (PPA) that modulates information access across agents in a network, optimizing social welfare and promoting pro-social behavior. Through validation in iterative games, including the prisoner dilemma, we demonstrate that SLA agents exhibit nuanced strategic adaptations. The PPA agent effectively learns to adjust information transparency, resulting in enhanced cooperation rates. This framework offers significant insights into AI-mediated social dynamics, contributing to the deployment of AI in real-world team settings.

The intricate dynamics of stock markets have led to extensive research on models that are able to effectively explain their inherent complexities. This study leverages the econometrics literature to explore the dynamic factor model as an interpretable model with sufficient predictive capabilities for capturing essential market phenomena. Although the model has been extensively applied for predictive purposes, this study focuses on analyzing the extracted loadings and common factors as an alternative framework for understanding stock price dynamics. The results reveal novel insights into traditional market theories when applied to the Philippine Stock Exchange using the Kalman method and maximum likelihood estimation, with subsequent validation against the capital asset pricing model. Notably, a one-factor model extracts a common factor representing systematic or market dynamics similar to the composite index, whereas a two-factor model extracts common factors representing market trends and volatility. Furthermore, an application of the model for nowcasting the growth rates of the Philippine gross domestic product highlights the potential of the extracted common factors as viable real-time market indicators, yielding over a 34% decrease in the out-of-sample prediction error. Overall, the results underscore the value of dynamic factor analysis in gaining a deeper understanding of market price movement dynamics.

Finding the mixed Nash equilibria (MNE) of a two-player zero sum continuous game is an important and challenging problem in machine learning. A canonical algorithm to finding the MNE is the noisy gradient descent ascent method which in the infinite particle limit gives rise to the {\em Mean-Field Gradient Descent Ascent} (GDA) dynamics on the space of probability measures. In this paper, we first study the convergence of a two-scale Mean-Field GDA dynamics for finding the MNE of the entropy-regularized objective. More precisely we show that for each finite temperature (or regularization parameter), the two-scale Mean-Field GDA with a suitable {\em finite} scale ratio converges exponentially to the unique MNE without assuming the convexity or concavity of the interaction potential. The key ingredient of our proof lies in the construction of new Lyapunov functions that dissipate exponentially along the Mean-Field GDA. We further study the simulated annealing of the Mean-Field GDA dynamics. We show that with a temperature schedule that decays logarithmically in time the annealed Mean-Field GDA converges to the MNE of the original unregularized objective.

As the open-weight AI landscape continues to proliferate-with model development, significant investment, and user interest-it becomes increasingly important to predict which models will ultimately drive innovation and shape AI ecosystems. Building on parallels with citation dynamics in scientific literature, we propose a framework to quantify how an open-weight model's influence evolves. Specifically, we adapt the model introduced by Wang et al. for scientific citations, using three key parameters-immediacy, longevity, and relative fitness-to track the cumulative number of fine-tuned models of an open-weight model. Our findings reveal that this citation-style approach can effectively capture the diverse trajectories of open-weight model adoption, with most models fitting well and outliers indicating unique patterns or abrupt jumps in usage.

In arena-style evaluation of large language models (LLMs), two LLMs respond to a user query, and the user chooses the winning response or deems the "battle" a draw, resulting in an adjustment to the ratings of both models. The prevailing approach for modeling these rating dynamics is to view battles as two-player game matches, as in chess, and apply the Elo rating system and its derivatives. In this paper, we critically examine this paradigm. Specifically, we question whether a draw genuinely means that the two models are equal and hence whether their ratings should be equalized. Instead, we conjecture that draws are more indicative of query difficulty: if the query is too easy, then both models are more likely to succeed equally. On three real-world arena datasets, we show that ignoring rating updates for draws yields a 1-3% relative increase in battle outcome prediction accuracy (which includes draws) for all four rating systems studied. Further analyses suggest that draws occur more for queries rated as very easy and those as highly objective, with risk ratios of 1.37 and 1.35, respectively. We recommend future rating systems to reconsider existing draw semantics and to account for query properties in rating updates.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.