Large language model agents are increasingly deployed in settings where the value of an action depends on what other agents do. This creates a strategic reliability problem: the same game may be described as a business negotiation, a friendly compromise, a diplomatic exchange, or an abstract payoff matrix, and the model may choose different actions even when the incentives are unchanged. This paper introduces \emph{Same Game, Different Story}, a benchmark for strategic robustness: invariance of model-induced action distributions under payoff-preserving language changes. The empirical analysis uses a deliberately narrow, literature-calibrated comparison from Lor`e and Heydari's peer-reviewed study: business framing versus friend-sharing framing across GPT-3.5, GPT-4, and LLaMa-2 in four social-dilemma games, with 300 initializations per retained model-game-context cell. The retained design comprises 24 of the source study's 60 cells, representing 7,200 decisions. Because trial-level files were not available from the article, the analysis is presented as a secondary calibration based on reconstructed published rates, not as new model runs. As a conservative sensitivity analysis, effect magnitudes are attenuated by 30% toward the null: action shifts are multiplied by 0.70, and non-robustness, defined as one minus the robustness score, is multiplied by 0.70. Under this attenuation, pooled strategic robustness is 0.783 with a 95% bootstrap interval from 0.774 to 0.790, and friend-sharing framing raises cooperation by 0.307 with a 95% bootstrap interval from 0.297 to 0.316 relative to business framing. The analysis supports the narrower claim that social-relational framing can change strategic choices even when incentives are held fixed, without extending the analysis to a broader suite of contextual or cross-benchmark comparisons.
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.
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.