Monte-Carlo Dual Bounds for Finite Horizon Zero-Sum Games

Abstract

We extend the duality approach of Haugh-Kogan and Rogers to two-player stochastic zero-sum stopping games where players have asymmetric information of the state space at each action time, and modify the Andersen-Broadie primal dual method to present a Monte-Carlo framework for estimating their optimal values. In addition, we provide a practical sub-simulation solution for evaluating general stochastic zero-sum games with symmetric information. The methods generate both lower and upper bounds for the optimal value, and hence give a valid confidence interval.