The Role of Network Topology and Opponent Information in Shaping Cooperation in Multi-Agent Reinforcement Learning Systems

Several works have investigated the influence of graph topology on cooperation among artificial agents, while the majority of the literature has focused on modelling agents' adaptation through strategy imitation, which relies solely on the cumulative payoffs of others. This paper investigates scenarios in which each agent learns to play the two-player Iterated Prisoner's Dilemma (IPD) using deep reinforcement learning. Each agent is represented as a node in a graph, where its neighbours constitute the pool of opponents with whom it can interact. During each IPD episode, agents are provided with different types of information about their opponent, consisting of action history and opponent identity. Experimental results across different graph topologies show that the number of neighbours per node and the average path length are the main factors affecting the emergence of cooperation. We also show that, while partner selection fosters mutual cooperation by limiting the diversity of the opponent pool, providing agents with the identity of their opponent hinders the proliferation of cooperative strategies.

Emergence of cooperation: A reputation-modulated reinforcement learning

Reputation is widely recognized as a key mechanism for sustaining cooperation. However, most existing game-theoretic models treat reputation primarily as an external factor that modulates payoffs, interaction structures, or strategy update rules. In many social contexts, though, reputation operates primarily as information -- it shapes how individuals interpret their own experiences and assess the behavior of others. To bridge this gap, we propose a spatial prisoner's dilemma game grounded in the reinforcement learning paradigm, in which agents equipped with Q-learning integrate both individual and social information via a locally defined reputation metric to guide their decisions. Our results reveal that reputation-modulated learning significantly promotes the emergence of cooperative behavior, and we observe a discontinuous phase transition from full cooperation to full defection as the temptation increases. Cooperation spreads through the nucleation of cooperative clusters, whereas the disintegration of these clusters drives the system into an absorbing state of complete defection. Overall, this study demonstrates that reputation facilitates cooperation not only by providing direct incentives but also by reshaping the social information landscape that agents rely on for learning and adaptation.

The Open-Strategy Dictator Game: Cooperation Under Mutual Transparency

We introduce the Open-Strategy Dictator Game (OSDG), a variant of the classic dictator game in which each player's strategy is a natural-language document visible to all participants. The dictator's decision, to SHARE or TAKE an endowment, may depend on the text of the recipient's strategy. A large language model adjudicates each interaction by interpreting the dictator's strategy in the context of the recipient's. We run round-robin tournaments among diverse strategies and analyze the resulting payoff matrix using softmax equilibrium frequencies, dominance analysis, and sensitivity to the relative value of cooperation. Conditionally cooperative strategies, those that share with cooperators and take from exploiters, consistently dominate, while unconditional strategies (always share or always take) are weakly dominated. The results suggest that in environments where agents can inspect each other's decision procedures, conditional cooperation is evolutionarily robust across a wide range of payoff parameters.

Do LLMs Take Care of Their Own? Similarity Signals Can Induce Cooperation

As LLM-based agents with user-instructed goals are becoming widely deployed, they increasingly encounter each other in strategic interactions, and face challenges of finding mutually beneficial outcomes. Prior literature has argued that cooperation problems such as the Prisoner's Dilemma are resolvable in settings where agents know they follow very similar decision making patterns, as for example in monocultural AI ecosystems. Following that line of work, this paper introduces the first framework for evaluating LLM decision making when agents are provided with graded similarity signals. Among our findings, we establish that different LLM models vary drastically in how they navigate similarity signals, with some modern models showing consistent behavior across cooperation problems, payoff structures, and prompt framing. Perhaps surprisingly, our experiments also show that the dataset based on which the similarity signal is computed has small to no impact on induced cooperation, and that LLM models systematically self-identify as highly similar when asked to evaluate another model's chain-of-thought reasoning by themselves. Finally, we develop an LLM-behavioral-game-theoretic model that captures some of their reasoning rationale, and show that it can support cooperative outcomes in equilibrium under sufficiently high similarity scores.

A game theory for foundation models shows new paths to rational cooperation through similarity inference

As autonomous agents powered by foundation models are increasingly integrated into social and economic systems, understanding the principles governing their collective behavior is essential for ensuring safety and cooperation. Classical game theory, the dominant framework for modeling rational interaction, is built upon the assumption of `decoupled agency,' where agents treat their own decision-making as independent of the environment and other actors. Modern AI agents, however, jointly predict their own future actions alongside external observations. Here, we report a striking finding: when interacting in stylized social dilemmas, foundation model agents engaging in optimal planning consistently converge to stable cooperation, directly contradicting classical game-theoretic predictions of mutual defection. To understand this phenomenon, we introduce the `embedded Bayesian agent,' a theoretical model for foundation model agents. By shifting from decoupled to embedded agency, these agents model themselves as part of the universe they inhabit, maintaining epistemic uncertainty about their own decision-making algorithms. We show that by inferring whether others are behaviorally similar, an embedded agent treats its own deliberation during planning as evidence: a decision to cooperate predicts a similar decision by a similar partner. We formalize this mechanism of similarity inference through the `embedded equilibrium,' a novel solution concept replacing the Nash equilibrium to provide a foundational game theory for the social behavior of modern AI agents.

Reputation-driven Cooperation in Lattice-based Decentralized Federated Learning through Evolutionary Game Theory

Decentralized Federated Learning (DFL) has emerged as an optimal privacy-preserving solution; however, it remains vulnerable to opportunistic behaviors due to the absence of a central coordinator. While Evolutionary Game Theory (EGT) serves as a powerful framework for analyzing such behaviors, existing studies often assume that agents possess perfect rationality and maintain static strategies. To address these limitations, this paper proposes a novel EGT framework designed to analyze strategic evolution and enhance overall system performance. The primary contributions of this work are threefold: First, we model peer-to-peer (P2P) interactions on a lattice network structure under the assumption of bounded rationality. Second, we formulate a comprehensive payoff matrix incorporating training costs, communication overhead, and cooperative rewards, while tailoring a strategy update rule that captures spatial propagation dynamics. Third, we integrate a reputation-based reward-and-punishment mechanism to effectively deter free-riding behaviors. Simulation results demonstrate that the framework significantly outperforms the baseline. Specifically, it increases average accuracy from approximately 70% to 82%, elevates cooperation frequency to approach 100% (compared to below 5% in the baseline), and drops accuracy variance from around 0.40 to 0.002, thereby accelerating uniform convergence and ensuring system stability.

Co-evolution of social reward and punishment under institutional interventions

We investigate how peer and institutional incentives jointly shape the evolution of cooperation, social welfare, and enforcement efficiency in social dilemmas. In a Prisoners Dilemma with four strategies, unconditional cooperators (C), defectors (D), social punishers (SP), and social rewarders (SR), we allow decentralised peer incentives and centralised institutional incentives to act simultaneously, with the institution able to reward or punish any subset of strategies. In infinite well-mixed populations, we analyse the resulting four-strategy replicator dynamics, and in structured populations we use agent-based simulations on square lattices to study spatial effects and network reciprocity. Intervention schemes are evaluated by equilibrium states and evolutionary flow for infinite well-mixed populations, by cooperation levels and social welfare for structured populations, defined as aggregate population payoff net of institutional cost. We find that peer punishment most strongly promotes cooperation, whereas peer reward is more beneficial for social welfare. Institutionally rewarding peer incentive strategies substantially improves both cooperation and welfare, while subsidising unconditional cooperators has little impact. Under institutional punishment, directly penalising defectors is the only consistently effective policy; punishing peer incentive strategies dismantles decentralised incentives, reduces cooperation, and harms social welfare, showing that maximising cooperation does not necessarily optimise overall societal benefit. Our findings provide design principles for institutions seeking to balance cooperation promotion with welfare maximisation.

Falling Behind Drives Unsafe Development in an Idealised AI Race Experiment

Technological races create tension between speed and safety: actors may gain by moving faster than competitors, even when risky development is harmful. This is prominent in debates about artificial intelligence (AI), where competitive pressure is often argued to incentivise riskier, less safety-conscious development. We study this using a framed behavioural experiment based on an idealised AI race, in which paired participants repeatedly chose between Safe and Unsafe development under an uncertain time horizon. Unsafe development gave faster progress and higher immediate payoffs but accumulated private risk up to a treatment-specific maximum of 10\%, 60\%, or 90\%; the race's competitive structure was held constant, and only this maximum risk varied. Neither the pre-registered comparison between risk levels nor the role of elicited risk preferences was supported by the data. Instead, exploratory analyses motivated by the task's repeated structure show that Unsafe behaviour is shaped less by risk preferences than by the evolving strategic state of the race: participants are more likely to choose Unsafe after their opponent does so, being ahead reduces Unsafe play while falling behind increases it, and first-round choices predict later behaviour. To interpret these effects we introduce a reduced evolutionary model with four strategies -- Always Safe, Always Unsafe, Conditionally Safe, and Conditionally Antisocial Safe -- which reproduces the treatment effect and shows how conditional Unsafe behaviour can be favoured by competitive race dynamics. Together, the experiment and model show that unsafe development can emerge from early behavioural momentum, opponent behaviour, and fear of falling behind, rather than from risk preferences alone, suggesting policy should focus on reducing competitive pressure and promoting cooperation in AI development rather than only individual risk.

Moral Hazard in Multi-Agent Language Models

Cooperation can fail when socially valuable effort is costly, weakly observable, and mainly benefits others. Drawing on Holmström's team moral-hazard model, we introduce the Dialogue Moral Hazard Game, a controlled textual game that operationalizes this hidden-action structure for language agents. In each episode, an agent can preserve an immediate local reward or pay a query cost to reveal a hidden safety fact that primarily helps another agent's downstream decision. We evaluate seven open-weight language models and decompose behavior into query use, realized information transfer, local-reward preservation, unsafe choice, format validity, and team success. Base models commonly preserve local reward without team success or query without communicating information that changes the final decision. We then use supervised fine-tuning, RLOO, sequential SFT+RLOO, and GEPA prompt optimization as diagnostic update mechanisms. Their effects are heterogeneous: OLMo-7B shows the clearest mechanism-consistent weight-level improvement, whereas GEPA sometimes improves team success while reducing or eliminating costly queries. Thus, optimization can shift aggregate reward without recovering the intended cooperative mechanism, motivating evaluations that report mechanism-level behavior rather than team success alone.

Integrated Altruistic and Fairness Preference Induces Advanced Mutual Cooperation in Sequential Social Dilemmas

Inducing cooperation among distributed agents is still a difficult problem in the field of multi-agent reinforcement learning (MARL), particularly in social dilemma situations. There, individual interests are misaligned with the common good and individual rationality leads to suboptimal group outcomes. In contrast, humans are able to achieve cooperation with one another in such situations. A common explanation for such cooperative behavior is that individuals have social preferences. In order to achieve cooperation in MARL, we design a new utility function integrating altruistic preferences (incentive for other's reward) and fairness preferences (incentive for equality) from social psychology and behavioral economics, namely, Altruistic and Fairness Preference (AFP), a reward-sharing mechanism which converts one's own and other's rewards to incentives for cooperative behavior. We performed comparative experiments with standard RL and inequity aversion agents in two challenging sequential social dilemma games, and showed that AFP agents successfully achieved mutual cooperation with more collective rewards and higher equity than the baselines. To further understand the progression of AFP during training, we subsequently explore the effects of altruistic preferences and fairness preferences on agents' behavior. The results suggest that altruistic preferences encourage agents to contribute to the public goods, and fairness preferences induce mutual behavior between agents.

MECoBench: A Systematic Study of Multimodal Agent Collaboration in Embodied Environments

Recent multimodal large language models (MLLMs) have strong potential as embodied agents, but their ability to collaborate in visually grounded environments remains underexplored. To address this gap, we introduce MECoBench, a multimodal embodied cooperation benchmark with an evaluation platform spanning diverse real-world tasks, two cooperation structures, and three collaboration modes. Through extensive experiments across various MLLMs, we summarize three key findings: (i) Collaboration generally improves embodied task completion, but its benefits depend on balancing collaborative gains against coordination complexity. (ii) Communication is essential to collaboration gains, while the best collaboration mode depends on team size and model capability. (iii) Moreover, collaboration improves robustness under noisy priors and exploration conditions. Generally, MECoBench provides a systematic testbed for understanding the mechanisms and limits of multimodal embodied collaboration. Code and dataset are available at https://github.com/q-i-n-g/MECoBench.

AI Persuasive Framing in Collective Dilemmas

AI agents are promising tools that can act as flexible behavioral nudges to enhance human cooperation in addressing large-scale societal problems. However, evidence on whether AI agents can effectively boost cooperation remains mixed. We recruited 1,283 participants to play iterated Collective Risk Games in small groups, testing whether AI assistants could nudge participants toward cooperation. By using persuasive framing personalized to each player's Social Value Orientation profile, the AI interventions significantly increased contributions and group success rates. These cooperative effects were short-lived, however, fading after the first few rounds. Strikingly, when the AI treatments were reconfigured to promote selfish behavior through exculpatory framing, the negative effects on contributions and group success were larger and substantially more persistent, particularly for personalized interventions. This asymmetry between prosocial and antisocial persuasion highlights the dual-use risks of AI systems designed to influence group behavior in collective action settings.

Parametric Open Source Games

Open-source game theory studies agents whose behavior may depend on one another's decision procedures, but most existing models use discrete or symbolic programs. We introduce parametric open-source games, a continuous analogue of program equilibria in which players choose parameter vectors and semantics maps convert the full parameter profile into mixed actions in an underlying finite game. We establish equilibrium existence results, derive an exact coupling threshold at which selfish gradient ascent in symmetric $2\times2$ games switches from defection toward cooperation, and give a one-dimensional boundary test for parametric program Nash equilibria. We further extend the framework to a neural semantics class whose first-order cooperation condition is governed by the ratio of cross-player to self-player sensitivity. Across canonical games, the framework shows how access to internal parameterizations can qualitatively reshape learning dynamics and equilibrium structure, and how sufficiently strong open-source coupling can steer selfish optimization toward cooperative outcomes.

Representational Similarity and Model Behavior in Multi-Agent Interaction

Researchers have shown that neural similarity among humans predicts social closeness and cooperative success, whereas innovation often emerges from interactions among dissimilar individuals. We investigate whether these principles extend to artificial intelligence by examining interactions between large language models. In our experiments, 276 model pairs interact across eight games spanning both cooperation and novelty. We find that pairs with more similar representation spaces achieve significantly higher cooperation but exhibit reduced novelty and creativity. The effects of representational similarity on cooperation and novelty remain robust even after controlling for other factors such as performance disparity and model size. We also find that similarity in the early layers consistently shows the strongest association with cooperation and novelty, compared to the middle and later layers. This suggests that a central factor underlying these patterns could be the extent to which the two models share lexical and semantic grounding. Overall, representational similarity can be an important consideration in multi-agent system design.

Solipsistic Superintelligence is Unlikely to be Cooperative

AI's central challenge is shifting from capability to coexistence. The dominant paradigm in AI research focuses on developing powerful agents that treat the world as an exogenous and stationary source of feedback. We contend that superintelligence, an extremely capable task solver, born out of such a solipsistic approach to AI design, is unlikely to be cooperative. Deploying AI systems induces endogenous non-stationarity, resulting in a train-test-deploy gap where historical distributions diverge from the deployment context. We refer to this as the self-undermining property of unilateral optimization. Closing this gap requires AI that participates in cooperation: the equilibrium-selection process through which multiple actors navigate their interdependence. We call for a non-solipsistic research paradigm that treats this interdependence as a core design principle rather than approaching cooperation as a task to solve. This entails building dynamic evaluation testbeds involving adaptive counterparties, treating institutions as design primitives, and preserving human agency as a structural feature of the systems we build.

Measuring Successful Cooperation in Human-AI Teamwork: Development and Validation of the Perceived Cooperativity and Teaming Perception Scales

As human-AI cooperation becomes increasingly prevalent, reliable instruments for assessing the subjective quality of cooperative human-AI interaction are needed. We introduce two theoretically grounded scales: the Perceived Cooperativity Scale (PCS), grounded in joint activity theory, and the Teaming Perception Scale (TPS), grounded in evolutionary cooperation theory. The PCS captures an agent's perceived cooperative capability and practice within a single interaction sequence; the TPS captures the emergent sense of teaming arising from mutual contribution and support. Both scales were adapted for human-human cooperation to enable cross-agent comparisons. Across three studies (N = 409) encompassing a cooperative card game, LLM interaction, and a decision-support system, analyses of dimensionality, reliability, and validity indicated that both scales successfully differentiated between cooperation partners of varying cooperative quality and showed construct validity in line with expectations. The scales provide a basis for empirical investigation and system evaluation across a wide range of human-AI cooperation contexts.