Not Just an Empty Threat: Subgame-Perfect Equilibrium in Repeated Games Played by Computationally Bounded Players

Abstract. We study the problem of finding a subgame-perfect equilibrium in re-peated games. In earlier work [Halpern, Pass and Seeman 2014], we showed how to efficiently find an (approximate) Nash equilibrium if assuming that players are computationally bounded (and making standard cryptographic hardness assump-tions); in contrast, as demonstrated in the work of Borgs et al. [2010], unless we restrict to computationally bounded players, the problem is PPAD-hard. But it is well-known that for extensive-form games (such as repeated games), Nash equilibrium is a weak solution concept. In this work, we define and study an ap-propriate notion of a subgame-perfect equilibrium for computationally bounded players, and show how to efficiently find such an equilibrium in repeated games (again, making standard cryptographic hardness assumptions). We also show that our algorithm works not only for games with a finite number of players, but also for constant-degree graphical games.