Finite State Machines Play Extensive-Form Games

Abstract

Finite state machines are a well-known representation of strategies in (in)finitely repeated or stochastic games. Actions of players correspond to states in the machine and the transition between machine-states are caused by observations in the game. For extensive-form games (EFGs), machines can act as a formal grounding for abstraction methods used for solving large EFGs and as a domain-independent approach for generating sufficiently compact abstractions. We show that using machines of a restricted size in EFGs can both (i) reduce the theoretical complexity of computing some solution concepts, including Strong Stackelberg Equilibrium (SSE), (ii) as well as bring new practical algorithms that compute near-optimal equilibria considering only a fraction of strategy space. Our contributions include (1) formal definition and theoretical characterization of machine strategies in EFGs, (2) formal definitions and complexity analysis for solution concepts and their computation when restricted to small classes of machines, (3) new algorithms for computing SSE in general-sum games and Nash Equilibrium in zero-sum games that both directly use the concept of machines. Experimental results on two different domains show that the algorithms compute near-optimal strategies and achieve significantly better scalability compared to previous state-of-the-art algorithms.