Doomsday Equilibria for Omega-Regular Games

TL;DR

This paper introduces doomsday equilibria in omega-regular games, providing algorithms and complexity bounds for their existence in both perfect and imperfect information settings, advancing understanding of strategic stability.

Contribution

It proposes doomsday equilibria, a new solution concept for omega-regular games, with algorithms and complexity analysis for their existence in various game classes.

Findings

Algorithms for deciding doomsday equilibria in imperfect-information games.

Optimal complexity bounds established for various game classes.

Applicability to both perfect and imperfect information games.

Abstract

Two-player games on graphs provide the theoretical frame- work for many important problems such as reactive synthesis. While the traditional study of two-player zero-sum games has been extended to multi-player games with several notions of equilibria, they are decidable only for perfect-information games, whereas several applications require imperfect-information games. In this paper we propose a new notion of equilibria, called doomsday equilibria, which is a strategy profile such that all players satisfy their own objective, and if any coalition of players deviates and violates even one of the players objective, then the objective of every player is violated. We present algorithms and complexity results for deciding the existence of doomsday equilibria for various classes of omega-regular objectives, both for imperfect-information games, and for perfect-information games. We provide optimal complexity bounds for imperfect-information games, and in most cases for perfect-information games.