CRISP: Critical-Manifold Informed Strategic Play for Multi-Agent LLM Social Simulation

Cooperation among self-interested learning agents is a central question for LLM-based social simulation, yet the online prompt-optimization tools that steer such agents are built for single learners against stationary environments. When the same online learner is deployed at every seat of a multi-agent conversation, opponent policies co-evolve, cooperation-inducing mechanisms lie outside the arm space, and hand-tuned exploration schedules leave agents locked into defect-dominant equilibria. We introduce CRISP (Critical-manifold Informed Strategic Play), a decentralized online learner that lets every LLM agent jointly search over behavioral strategies and textual mechanism proposals (repetition, reputation, mediation, contract), and that drives the sampling temperature, step size, and recency factor from the empirical distance to a phase-transition manifold estimated online. Under this construction, the exponential-weights potential admits a formal analysis: individual regret is $\mathcal{O}(\sqrt{TK\log K})$ up to a surrogate approximation term, and the empirical joint play of all agents converges to an $\mathcal{O}(\sqrt{K\log K/T})$-coarse-correlated equilibrium, without any communication among agents. A physics-inspired controller derived from a Curie–Weiss free energy concentrates exploration precisely where a per-turn reward has non-trivial influence on the collective norm, preserving the convergence rate while eliminating manual scheduling. We specify an evaluation on Sotopia and CoopEval, spanning seven social dimensions and four social dilemmas, with component ablations designed to test whether CRISP improves cooperation under co-adaptive partners.