Solving two-state Markov games with incomplete information on one side

Abstract

We study the optimal use of information in Markov games with incomplete information on one side and two states. We provide a finite-stage algorithm for calculating the limit value as the gap between stages goes to 0, and an optimal strategy for the informed player in the limiting game in continuous time. This limiting strategy induces an ϵ-optimal strategy for the informed player, provided the gap between stages is small. Our results demonstrate when the informed player should use her information and how.