The Complexity of Admissibility in Omega-Regular Games

TL;DR

This paper investigates the computational complexity of iterated admissibility in omega-regular infinite games on graphs, providing exact complexity results and automata constructions for strategy outcomes.

Contribution

It establishes the precise complexity of decision problems related to strategy elimination and outcome recognition in omega-regular games, extending classical game theory concepts.

Findings

Determined the exact complexity of strategy elimination problems.

Constructed automata recognizing all possible strategy outcomes.

Extended classical admissibility concepts to infinite graph games.

Abstract

Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games played on graphs with omega-regular objectives. In this paper, we study the algorithmic properties of this concept for such games. We settle the exact complexity of natural decision problems on the set of strategies that survive iterated elimination of dominated strategies. As a byproduct of our construction, we obtain automata which recognize all the possible outcomes of such strategies.