Pure Nash Equilibria in Concurrent Deterministic Games

TL;DR

This paper introduces the suspect game construction to transform multi-player concurrent deterministic games into two-player turn-based games, enabling efficient computation of pure Nash equilibria across various preference relations.

Contribution

It presents a novel suspect game method that converts multi-player games into two-player turn-based games, facilitating the analysis and computation of Nash equilibria with optimal complexity.

Findings

The suspect game transformation effectively finds Nash equilibria in finite games.

Algorithms achieve optimal worst-case complexity for a broad class of preferences.

Applicable to both qualitative and semi-quantitative omega-regular objectives.

Abstract

We study pure-strategy Nash equilibria in multi-player concurrent deterministic games, for a variety of preference relations. We provide a novel construction, called the suspect game, which transforms a multi-player concurrent game into a two-player turn-based game which turns Nash equilibria into winning strategies (for some objective that depends on the preference relations of the players in the original game). We use that transformation to design algorithms for computing Nash equilibria in finite games, which in most cases have optimal worst-case complexity, for large classes of preference relations. This includes the purely qualitative framework, where each player has a single omega-regular objective that she wants to satisfy, but also the larger class of semi-quantitative objectives, where each player has several omega-regular objectives equipped with a preorder (for instance, a player may want to satisfy all her objectives, or to maximise the number of objectives that she achieves.)