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

• URL: http://arxiv.org/abs/2609.02750v1
• Date: Wed, 02 Sep 2026 15:50:10 GMT
• Title: Bilevel Coordinated Reflection: A Game-Theoretic Approach to Multi-Agent LLM Systems
• Abstract summary: Multi-agent LLM systems commonly use an orchestrator to decompose a task for a team of workers and then improve through textual reflection.<n>Despite strong empirical results, these systems lack a unified account of coordination, memory improvement, and the role of external verification.<n>We provide confidence gating for evaluation and re-anchoring guarantees for piecewise-stationary environments.<n>Experiments instantiate these objects with environment-grounded metrics and test the predicted coordination and drift laws.
• Score: 40.47928908205563
• License: http://creativecommons.org/licenses/by/4.0/
• 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

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