Bilevel Coordinated Reflection: A Game-Theoretic Approach to Multi-Agent LLM Systems

Yihang Chen; Yuxiang Chen; Yuxuan Huang; Meng Fang; Weilin Luo; Jun Wang

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Paper · arXiv 2609.02750

Bilevel Coordinated Reflection: A Game-Theoretic Approach to Multi-Agent LLM Systems

Yihang Chen, Yuxiang Chen, Yuxuan Huang, Meng Fang, Weilin Luo, Jun Wang

141 upvotesSeptember 2, 2026arXiv 预印本

AI 摘要

The study formalizes multi-agent LLM coordination via bilevel games and stochastic memory reflection, introducing a grounded evaluation gate and SRMA algorithm with convergence guarantees, validated on SWE-bench.

bilevel coordination gameapproximate potential gamestochastic movementsemantic memory statesfalsifiable persistent-harm conditioninformation-theoretic impossibilitytext-indistinguishable environmentsenvironment-grounded gateStochastic Reflective Memory Ascentevaluation risknon-degenerate corrective masspiecewise-stationary environments

Abstract

Multi-agent LLM systems commonly use an orchestrator to decompose a task for a team of workers and then improve through textual reflection. Despite strong empirical results, these systems lack a unified account of coordination, memory improvement, and the role of external verification. We model orchestrator-worker interaction as a bilevel coordination game: under bounded coupling, the workers' local-update game is an approximate potential game whose equilibrium slack is controlled by decomposition quality. We then analyse reflection as stochastic movement over semantic memory states. For free-form reflection, we derive a finite-time upper bound, prove worst-case tightness, and give a positive lower bound under a falsifiable persistent-harm condition. We further prove an information-theoretic impossibility result: no gate that observes only the generated transcript can improve uniformly over text-indistinguishable environments, whereas an environment-grounded gate can. Motivated by this separation, we introduce Stochastic Reflective Memory Ascent (SRMA), which accepts a candidate memory only after a grounded evaluation risk strictly decreases. Under calibration and non-degenerate corrective mass, SRMA converges exactly, geometrically or polynomially; matching constructions show that both rate regimes are order-tight. We also provide confidence gating for stochastic evaluation and re-anchoring guarantees for piecewise-stationary environments. Experiments instantiate these objects with environment-grounded metrics and test the predicted coordination and drift laws. On 500 SWE-bench instances, the complete Kimi-based system resolves 72.2% versus a 70.8% public mini-SWE-agent reference. Code: https://github.com/YihangChen9/Bilevel-Coordinated-Reflection