An LLM agent-based framework for analytical characterization of Nash equilibria

In this paper, we introduce PrimeNash, a large language model agent framework that, to our knowledge, is the first to automatically derive closed-form Nash equilibria with machine-checkable proofs. PrimeNash decomposes equilibrium search into three modules, strategy generation, payoff evaluation, and equilibrium proof, and it couples multi-agent reasoning with symbolic code execution to handle high-dimensional strategies, intertemporal recursion, and discontinuous, non-convex payoffs. Across seven canonical models, PrimeNash solves all static games and 70% of dynamic games in which success is defined as obtaining a symbolic closed-form solution that passes automated equilibrium checks. Notably, it produces the first analytical solution to a carbon market model previously lacking a closed-form characterization. The framework reduces manual derivation effort while preserving reproducibility and auditability through generated code and proof artifacts. By turning equilibrium derivation from a bespoke manual exercise into a transparent, scalable pipeline, PrimeNash extends the toolkit for economic analysis and opens new avenues for studying complex strategic systems from climate policy to financial markets. Broader context: Deriving Nash equilibrium supports decision analysis in economics, energy systems, and public policy, yet traditional analytical methods fail when facing high-dimensional, non-convex, or dynamic games. PrimeNash pioneers the use of large language model agents to automatically derive and verify closed-form equilibria, converting equilibrium search from a manual exercise into a reproducible computational process. By integrating symbolic reasoning, code execution, and formal proof, it bridges AI reasoning with mathematical rigor. This breakthrough reduces the human effort required for equilibrium derivation by more than 80% while maintaining interpretability and auditability. Beyond methodological innovation, PrimeNash empowers transparent modeling of strategic interactions in carbon markets, energy systems, and regulatory design, which are areas critical for climate mitigation and economic resilience. Its agent-based framework marks a foundational step toward AI-driven scientific discovery in game theory and economics, opening pathways to scalable policy analysis and automated theorem-assisted research.