Stability and Optimality of Two Players Zero-Sum Stochastic Adaptive Games

In this paper, we consider two players zero-sum adaptive games described by a linear discrete-time input-output stochastic model with unknown parameters, especially “high frequency gains”. The players apply the idea of adaptive control to design the strategy profile aiming to optimize one-step-ahead output-tracking quadratic payoff function. We assume that the players estimate the unknowns with the weighted least-squares algorithm, and substitute the unknowns in the optimal action with the estimations to obtain the adaptive strategies. We will prove that with the idea of the adaptive control, the strategy profile can make the system globally stable and is an asymptotic Nash equilibrium to our game problems.