Beyond Symmetry in Repeated Games with Restarts

2025-05-20

AI Summary

This paper investigates equilibrium modeling and strategy incentive design in asymmetric repeated games augmented with a “restart” mechanism—where players may unilaterally terminate their current match and be randomly rematched with a new opponent. We establish the first theoretical framework for equilibria in asymmetric restart games, characterizing necessary and sufficient conditions under which a target strategy profile can be implemented as a subgame-perfect equilibrium. We prove that computing a cost-optimal target sequence is NP-hard in general. For the objective of maximizing social welfare, we devise a pseudo-polynomial-time dynamic programming algorithm. Our core contributions are threefold: (i) extending restart game theory to asymmetric settings; (ii) deriving implementability criteria grounded in subgame-perfect equilibrium refinement; and (iii) delineating the computational complexity boundary—establishing hardness in the general case while identifying tractable special cases amenable to efficient optimization.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Extend equilibria analysis to asymmetric repeated games with restarts
• Characterize incentivizable goal strategies in equilibrium settings
• Study NP-hard computational problem of minimal-cost action sequences

Innovation

• Extend equilibria in asymmetric restart games
• Characterize goal strategies for player incentives
• Develop pseudo-polynomial algorithm for welfare