Dynamic Belief State Planning Framework for Ambush Avoidance in Contested Environments: A Game-Theoretic Approach

Abstract Existing approaches to adversarial path planning for ambush avoidance assume perfect, static information about opponent strategies and environmental conditions—an assumption that fails in dynamic settings where information degrades and adaptive agents learn from observed behavioral patterns. We present a dynamic belief state planning framework that extends game-theoretic path planning through four multiplicative adjustment factors modeling temporal information decay, opponent adaptation through strategy learning, environmental uncertainty propagation, and partial observability constraints. The framework operates in belief space rather than state space while maintaining polynomial-time computational complexity through linear programming formulations with temporally-adjusted utility values. Validation across 180 simulated scenarios demonstrates that our dynamic belief planning approach maintains 95% of optimal performance under severe information degradation conditions where static game-theoretic approaches degrade to 6% effectiveness—representing an 89 percentage point improvement in decision quality. The framework establishes critical operational thresholds for autonomous agents: active information gathering becomes beneficial above environmental uncertainty U=0.36, behavioral strategies with entropy below 0.3 enable opponent exploitation through learning, and extended planning horizons exceeding 20 decision epochs require 15-20% performance degradation margins. The framework provides computationally tractable solutions for autonomous agent deployment while bridging theoretical optimality and practical realizability for agents operating under degraded observability and adaptive opponents.