Beyond Symmetry in Repeated Games with Restarts

TL;DR

This paper extends the concept of repeated games with restarts to asymmetric settings, characterizing equilibrium strategies, analyzing their incentives, and addressing the computational complexity of finding optimal strategies.

Contribution

It introduces and analyzes more general equilibria in asymmetric repeated games with restarts, beyond the symmetric case studied previously.

Findings

Characterization of incentivized goal strategies in equilibrium.

NP-hardness of finding minimal-cost action sequences.

Pseudo-polynomial time algorithm for social welfare maximization.

Abstract

Infinitely repeated games support equilibrium concepts beyond those present in one-shot games (e.g., cooperation in the prisoner's dilemma). Nonetheless, repeated games fail to capture our real-world intuition for settings with many anonymous agents interacting in pairs. Repeated games with restarts, introduced by Berker and Conitzer [IJCAI '24], address this concern by giving players the option to restart the game with someone new whenever their partner deviates from an agreed-upon sequence of actions. In their work, they studied symmetric games with symmetric strategies. We significantly extend these results, introducing and analyzing more general notions of equilibria in asymmetric games with restarts. We characterize which goal strategies players can be incentivized to play in equilibrium, and we consider the computational problem of finding such sequences of actions with minimal cost for the agents. We show that this problem is NP-hard in general. However, when the goal sequence maximizes social welfare, we give a pseudo-polynomial time algorithm.