This paper introduces a formal game-theoretic framework to model orchestrator-worker interactions in multi-agent LLM systems as a bilevel coordination game. The researchers demonstrate that under bounded coupling, workers' local-update games function as approximate potential games, where equilibrium slack is determined by the quality of task decomposition. To optimize memory, the authors treat reflection as stochastic movement across semantic memory states, providing a finite-time upper bound for free-form reflection and proving its tightness. A key theoretical contribution is an information-theoretic impossibility result stating that gates observing only generated transcripts cannot improve performance in text-indistinguishable environments; conversely, environment-grounded gates can. To address this, the authors propose Stochastic Reflective Memory Ascent (SRMA), a method that only accepts candidate memory updates when a grounded evaluation risk shows a strict decrease. They prove that SRMA achieves exact convergence—either geometrically or polynomially—under specific calibration and non-degenerate corrective mass conditions. Experimental validation on 500 SWE-bench instances demonstrates the efficacy of this approach, with a Kimi-based implementation achieving a 72.2% resolution rate, outperforming the 70.8% benchmark set by the public mini-SWE-agent reference. The framework also includes confidence gating for stochastic evaluations and re-anchoring guarantees for piecewise-stationary environments.