Can cooperation among large language model (LLM) agents be evolutionarily stable against free-rider invasion? We study an indirect reciprocity donation game where LLM agents observe behavioral traces and donate on a continuous scale. Strategies, represented as natural language prompts, evolve through cultural transmission across generations. Across four LLM backends, robustness to free-rider invasion varies by more than an order of magnitude. The strongest predictor of this robustness is opponent endowment sensitivity, the degree to which agents discriminate between cooperative and uncooperative opponents, operationalizing the classical Image Scoring mechanism. By contrast, adherence to the Leading-Eight L1 norm does not predict robustness. Robustness depends on defector exclusion: while both cooperator reward and defector punishment vary across models, only the stringency of defector exclusion predicts resistance to free-rider invasion. These findings reveal that LLM agents are confined to Image Scoring-like discrimination and fail to develop the more robust Leading-Eight norms, highlighting a fundamental vulnerability in culturally evolved LLM cooperation and motivating bottom-up approaches to norm construction.
It is increasingly important that LLM agents interact effectively and safely with other goal-pursuing agents, yet, recent works report the opposite trend: LLMs with stronger reasoning capabilities behave less cooperatively in mixed-motive games such as the prisoner's dilemma and public goods settings. Indeed, our experiments show that recent models -- with or without reasoning enabled -- consistently defect in single-shot social dilemmas. To tackle this safety concern, we present the first comparative study of game-theoretic mechanisms designed to enable cooperative outcomes between rational agents in equilibrium. Across four social dilemmas testing distinct components of robust cooperation, we evaluate four families of mechanisms: (1) repeating the game for many rounds, (2) reputation systems, (3) third-party mediators to delegate decision making to, and (4) contract agreements for outcome-conditional payments between players. Among our findings, we establish that contracting and mediation are most effective in achieving cooperative outcomes between capable LLM models, and that repetition-induced cooperation deteriorates drastically when co-players vary. Moreover, we demonstrate that the mechanisms become more effective under evolutionary pressures to maximize individual payoffs.
Emanuel Tewolde, Xiao Zhang, David Guzman Piedrahita +2
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.
Do next-generation LLM agents inherit the cooperative biases documented in their predecessors, or does scale and provider diversity reshape equilibrium behaviour in competitive multi-agent settings? Willis et al. established a benchmark for this question using evolutionary game theory and the Iterated Prisoner's Dilemma (IPD), finding consistent cooperative biases in ChatGPT-4o and Claude 3.5 Sonnet. We extend this benchmark to four frontier models released in 2025-2026 - Claude Sonnet 4.6, Gemini 2.5 Flash, Gemini 3.1 Pro, and GPT-5.4 Mini - applying the identical protocol across three prompting styles (Default, Prose, Self-Refine) and four population compositions (balanced and biased, with and without noise). Cooperative bias persists across providers (H1): ten of twelve model-prompt combinations favour cooperative equilibria in balanced noiseless conditions. Cross-provider divergence is substantial (H3): Gemini 2.5 Flash reaches up to 77% aggressive equilibria under biased conditions, while GPT-5.4 Mini reaches 70% cooperative equilibria under Self-Refine. Support for aggressive capability parity is partial (H2): Self-Refine raises ICD in all models and Gemini 3.1 Pro Refine achieves the highest ICD in the dataset (0.925), but Default and Prose prompts show no systematic narrowing. Evidence on noise robustness is directionally positive but not robustly confirmed (H4): with n=500 Moran iterations per condition, average noise sensitivity is about 6 percentage points for Claude Sonnet 4.6 versus 13 pp for Claude 3.5 Sonnet, but this cross-study gap is not statistically significant once the predecessor's unreported sampling error is propagated. Provider identity, rather than model generation, is the strongest correlate of equilibrium outcomes; noise remains a universal challenge regardless of model size or vintage.