Adaptive Nash Strategies for Pursuit-Evasion Stochastic Games

This paper studies the stochastic adaptive game, focusing on the question of how to design adaptive strategies for linear systems of the pursuit-evasion game with quadratic indexes when the internal parameters of the systems are unknown. Specifically, we first use the least squares estimation algorithms to estimate the unknown parameter, and then by the so-called “certainty equivalence principle”, the players using their own parameter estimators construct the adaptive strategy profile. At last, we prove that the adaptive strategic profile guarantees global stability of the system, and reaches an asymptotic Nash equilibrium solution.