Measuring Competition and Cooperation in LLM Bargaining: An Empirical Meta-Game Analysis

We conduct an empirical game-theoretic analysis of how large-language models negotiate the division of a set of subjectively valued items.The LLM agents represent $\textit{meta-strategies}$, mapping a prompt describing the bargaining scenario to their implemented strategy for negotiation. To evaluate their relative performance, we formulate and estimate an empirical $\textit{meta-game}$ model over the LLM agents.We identify equilibria in this game model, and analyze the agents' competitiveness and fairness in the equilibrium context according to measures of regret, welfare, and envy-freeness. Uncertainty in these estimates is quantified using a statistical bootstrapping approach.Across nine LLM variants plus RL and heuristic baselines, OpenAI models (o3-mini, GPT-4o) deliver the best welfare–fairness trade-off and lowest exploitability. A rigid, Tough strategy exposes systematic weaknesses in Gemini and Claude models, underscoring the value of adversarial evaluation. Analysis of gradations of prompts shows that incremental strategic guidance reduces blatant mistakes.