GAMMA-LLM: Game-Theoretic Adaptive Multi-Agent Message Allocation for LLM Reasoning

Multi-agent large language model systems can improve reasoning by combining independent hypotheses and intermediate feedback, but additional communication is not uniformly beneficial: redundant or poorly targeted interactions increase inference-time token usage and can propagate incorrect rationales. We propose GAMMA, a game-theoretic framework for adaptive multi-agent message allocation that estimates which agents should receive greater influence and which communication edges have positive marginal value under a specified communication objective. GAMMA models agents as players in a graph-restricted cooperative game, constructs offline supervision from node-level Myerson contributions and cost-aware conditional edge values, and amortizes these quantities into a lightweight graph policy for sparse communication and contribution-weighted aggregation. Across nine reasoning benchmarks, GAMMA achieves higher macro-averaged accuracy than the evaluated adaptive multi-agent baselines while using fewer online inference tokens. Ablation, calibration, and robustness analyses further show improved prediction of the game-derived targets, lower error propagation, and fewer wrong-consensus failures.