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.

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.

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.

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.