Sound Algorithms in Imperfect Information Games

Abstract: Search has played a fundamental role in computer game research since the very beginning. And while online search has been commonly used in perfect information games such as Chess and Go, online search methods for imperfect information games have only been introduced relatively recently. This paper addresses the question of what is a sound online algorithm in an imperfect information setting of two-player zero-sum games? We argue that the fixed-strategy definitions of exploitability and epsilon-Nash equilibria are ill suited to measure the worst-case performance of an online algorithm. We thus formalize epsilon-soundness, a concept that connects the worst-case performance of an online algorithm to the performance of an epsilon-Nash equilibrium. Our definition of soundness and the consistency hierarchy finally provide appropriate tools to analyze online algorithms in repeated imperfect information games. We thus inspect some of the previous online algorithms in a new light, bringing new insights into their worst case performance guarantees.