Strategic Learning Under Linguistic and Contextual Constraints: A Theoretical Framework for LLM-Based Multi-Agent Coordination

Modern AI systems increasingly employ multiple language-based agents to solve complex problems. However, these systems face coordination challenges that traditional game theory cannot adequately address. AI agents have limited memory and must communicate through potentially ambiguous natural language. This paper develops two mathematical frameworks for multi-agent AI coordination. Context-Constrained Nash Equilibrium (CCNE) analyzes how memory limitations affect strategic decisions. Linguistic Uncertainty Games (LUG) models coordination under communication uncertainty. The analysis reveals critical findings. System performance undergoes dramatic changes at approximately 4,096 tokens—a threshold separating effective from ineffective coordination. Communication uncertainty strongly reduces coordination success (r = -0.85). Validation through 4,200 experimental trials across multiple benchmarks confirms these predictions. Systems using the proposed frameworks achieve 18.7% better performance than existing approaches (Cohen’s d = 1.24, p < 0.001). Results provide practical guidelines for designing effective AI coordination systems and reveal fundamental principles governing intelligent agent collaboration under realistic constraints.