Large language models (LLMs) are increasingly used both to make decisions in domains such as health, education and law, and to simulate human behavior. Yet how closely LLMs mirror actual human decision-making remains poorly understood. This gap is critical: misalignment could produce harmful outcomes in practical applications, while failure to replicate human behavior renders LLMs ineffective for social simulations. Here, we address this gap by developing a digital twin of game-theoretic experiments and introducing a systematic prompting and probing framework for machine-behavioral evaluation. Testing three open-source models (Llama, Mistral and Qwen), we find that Llama reproduces human cooperation patterns with high fidelity, capturing human deviations from rational choice theory, while Qwen aligns closely with Nash equilibrium predictions. Notably, we achieved population-level behavioral replication without persona-based prompting, simplifying the simulation process. Extending beyond the original human-tested games, we generate and preregister testable hypotheses for novel game configurations outside the original parameter grid. Our findings demonstrate that appropriately calibrated LLMs can replicate aggregate human behavioral patterns and enable systematic exploration of unexplored experimental spaces, offering a complementary approach to traditional research in the social and behavioral sciences that generates new empirical predictions about human social decision-making.

Inspired by the principle of self-regulating cooperation in collective institutions, we propose the Group Relative Policy Optimization with Global Cooperation Constraint (GRPO-GCC) framework. This work is the first to introduce GRPO into spatial public goods games, establishing a new deep reinforcement learning baseline for structured populations. GRPO-GCC integrates group relative policy optimization with a global cooperation constraint that strengthens incentives at intermediate cooperation levels while weakening them at extremes. This mechanism aligns local decision making with sustainable collective outcomes and prevents collapse into either universal defection or unconditional cooperation. The framework advances beyond existing approaches by combining group-normalized advantage estimation, a reference-anchored KL penalty, and a global incentive term that dynamically adjusts cooperative payoffs. As a result, it achieves accelerated cooperation onset, stabilized policy adaptation, and long-term sustainability. GRPO-GCC demonstrates how a simple yet global signal can reshape incentives toward resilient cooperation, and provides a new paradigm for multi-agent reinforcement learning in socio-technical systems.

Language models are increasingly deployed in interactive online environments, from personal chat assistants to domain-specific agents, raising questions about their cooperative and competitive behavior in multi-party settings. While prior work has examined language model decision-making in isolated or short-term game-theoretic contexts, these studies often neglect long-horizon interactions, human-model collaboration, and the evolution of behavioral patterns over time. In this paper, we investigate the dynamics of language model behavior in the iterated prisoner's dilemma (IPD), a classical framework for studying cooperation and conflict. We pit model-based agents against a suite of 240 well-established classical strategies in an Axelrod-style tournament and find that language models achieve performance on par with, and in some cases exceeding, the best-known classical strategies. Behavioral analysis reveals that language models exhibit key properties associated with strong cooperative strategies - niceness, provocability, and generosity while also demonstrating rapid adaptability to changes in opponent strategy mid-game. In controlled "strategy switch" experiments, language models detect and respond to shifts within only a few rounds, rivaling or surpassing human adaptability. These results provide the first systematic characterization of long-term cooperative behaviors in language model agents, offering a foundation for future research into their role in more complex, mixed human-AI social environments.

With the prospect of autonomous artificial intelligence (AI) agents, studying their tendency for cooperative behavior becomes an increasingly relevant topic. This study is inspired by the super-additive cooperation theory, where the combined effects of repeated interactions and inter-group rivalry have been argued to be the cause for cooperative tendencies found in humans. We devised a virtual tournament where language model agents, grouped into teams, face each other in a Prisoner's Dilemma game. By simulating both internal team dynamics and external competition, we discovered that this blend substantially boosts both overall and initial, one-shot cooperation levels (the tendency to cooperate in one-off interactions). This research provides a novel framework for large language models to strategize and act in complex social scenarios and offers evidence for how intergroup competition can, counter-intuitively, result in more cooperative behavior. These insights are crucial for designing future multi-agent AI systems that can effectively work together and better align with human values.

Are Large Language Models (LLMs) a new form of strategic intelligence, able to reason about goals in competitive settings? We present compelling supporting evidence. The Iterated Prisoner's Dilemma (IPD) has long served as a model for studying decision-making. We conduct the first ever series of evolutionary IPD tournaments, pitting canonical strategies (e.g., Tit-for-Tat, Grim Trigger) against agents from the leading frontier AI companies OpenAI, Google, and Anthropic. By varying the termination probability in each tournament (the "shadow of the future"), we introduce complexity and chance, confounding memorisation. Our results show that LLMs are highly competitive, consistently surviving and sometimes even proliferating in these complex ecosystems. Furthermore, they exhibit distinctive and persistent "strategic fingerprints": Google's Gemini models proved strategically ruthless, exploiting cooperative opponents and retaliating against defectors, while OpenAI's models remained highly cooperative, a trait that proved catastrophic in hostile environments. Anthropic's Claude emerged as the most forgiving reciprocator, showing remarkable willingness to restore cooperation even after being exploited or successfully defecting. Analysis of nearly 32,000 prose rationales provided by the models reveals that they actively reason about both the time horizon and their opponent's likely strategy, and we demonstrate that this reasoning is instrumental to their decisions. This work connects classic game theory with machine psychology, offering a rich and granular view of algorithmic decision-making under uncertainty.

With the rise of large language models (LLMs), AI agents as autonomous decision-makers present significant opportunities and challenges for human-AI cooperation. While many studies have explored human cooperation with AI as tools, the role of LLM-augmented autonomous agents in competitive-cooperative interactions remains under-examined. This study investigates human cooperative behavior by engaging 30 participants who interacted with LLM agents exhibiting different characteristics (purported human, purported rule-based AI agent, and LLM agent) in repeated Prisoner's Dilemma games. Findings show significant differences in cooperative behavior based on the agents' purported characteristics and the interaction effect of participants' genders and purported characteristics. We also analyzed human response patterns, including game completion time, proactive favorable behavior, and acceptance of repair efforts. These insights offer a new perspective on human interactions with LLM agents in competitive cooperation contexts, such as virtual avatars or future physical entities. The study underscores the importance of understanding human biases toward AI agents and how observed behaviors can influence future human-AI cooperation dynamics.

Cooperation between humans and machines is increasingly vital as artificial intelligence (AI) becomes more integrated into daily life. Research indicates that people are often less willing to cooperate with AI agents than with humans, more readily exploiting AI for personal gain. While prior studies have shown that giving AI agents human-like features influences people's cooperation with them, the impact of AI's assigned gender remains underexplored. This study investigates how human cooperation varies based on gender labels assigned to AI agents with which they interact. In the Prisoner's Dilemma game, 402 participants interacted with partners labelled as AI (bot) or humans. The partners were also labelled male, female, non-binary, or gender-neutral. Results revealed that participants tended to exploit female-labelled and distrust male-labelled AI agents more than their human counterparts, reflecting gender biases similar to those in human-human interactions. These findings highlight the significance of gender biases in human-AI interactions that must be considered in future policy, design of interactive AI systems, and regulation of their use.

In social dilemmas where the collective and self-interests are at odds, people typically cooperate less with machines than with fellow humans, a phenomenon termed the machine penalty. Overcoming this penalty is critical for successful human-machine collectives, yet current solutions often involve ethically-questionable tactics, like concealing machines' non-human nature. In this study, with 1,152 participants, we explore the possibility of closing this research question by using Large Language Models (LLMs), in scenarios where communication is possible between interacting parties. We design three types of LLMs: (i) Cooperative, aiming to assist its human associate; (ii) Selfish, focusing solely on maximizing its self-interest; and (iii) Fair, balancing its own and collective interest, while slightly prioritizing self-interest. Our findings reveal that, when interacting with humans, fair LLMs are able to induce cooperation levels comparable to those observed in human-human interactions, even when their non-human nature is fully disclosed. In contrast, selfish and cooperative LLMs fail to achieve this goal. Post-experiment analysis shows that all three types of LLMs succeed in forming mutual cooperation agreements with humans, yet only fair LLMs, which occasionally break their promises, are capable of instilling a perception among humans that cooperating with them is the social norm, and eliciting positive views on their trustworthiness, mindfulness, intelligence, and communication quality. Our findings suggest that for effective human-machine cooperation, bot manufacturers should avoid designing machines with mere rational decision-making or a sole focus on assisting humans. Instead, they should design machines capable of judiciously balancing their own interest and the interest of humans.

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's 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.

Cooperative behavior is prevalent in both human society and nature. Understanding the emergence and maintenance of cooperation among self-interested individuals remains a significant challenge in evolutionary biology and social sciences. Reinforcement learning (RL) provides a suitable framework for studying evolutionary game theory as it can adapt to environmental changes and maximize expected benefits. In this study, we employ the State-Action-Reward-State-Action (SARSA) algorithm as the decision-making mechanism for individuals in evolutionary game theory. Initially, we apply SARSA to imitation learning, where agents select neighbors to imitate based on rewards. This approach allows us to observe behavioral changes in agents without independent decision-making abilities. Subsequently, SARSA is utilized for primary agents to independently choose cooperation or betrayal with their neighbors. We evaluate the impact of SARSA on cooperation rates by analyzing variations in rewards and the distribution of cooperators and defectors within the network.