The Open-Strategy Dictator Game: Cooperation Under Mutual Transparency

2026-08-14

AI Summary

This study addresses the evolutionary stability of agent cooperation under transparent strategies by proposing an Open Strategy Dictator Game framework that leverages large language models to adjudicate natural language strategy interactions. Through round-robin tournaments, Softmax equilibrium analysis, and dominance evaluation, we systematically validate the evolutionary advantages of conditional cooperation strategies. Results demonstrate that across diverse parameter settings, conditional cooperation consistently outperforms unconditional strategies, exhibiting significant evolutionary robustness. By innovatively introducing natural language strategy visibility, this work elucidates the foundational mechanisms underlying the stability of conditional cooperation in transparent environments, offering new insights into how interpretability influences cooperative dynamics in multi-agent systems.

Abstract

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.

Problem

• Open-Strategy Dictator Game
• Mutual Transparency
• Conditional Cooperation
• Evolutionary Robustness

Innovation

• Open-Strategy Dictator Game
• Natural Language Strategy
• LLM Adjudication
• Conditional Cooperation
• Mutual Transparency