LP formulation of stochastic Bayesian two‐player zero‐sum games with long horizon

Abstract

AbstractThis article studies two‐player zero‐sum stochastic Bayesian games where each player has its own dynamic state that is unknown to the other. To compute the optimal strategy for the players, prior work uses sequence form to construct linear programming formulation, whose size grows exponentially with respect to the time horizon of the game. The exponential computational complexity restricts us in games with short horizon. While window‐by‐window or receding horizon methods can be used to extend the horizon, how to update the initial parameters in each window is still unknown. Based on the existing results about dual games, this article proposes LP formulations to update the initial parameters in each window. A window‐by‐window method is given with performance analysis. The main results are demonstrated in a security problem of underwater sensor networks.