Stochastic Equilibria under Imprecise Deviations in Terminal-Reward Concurrent Games

• Main Authors: Patricia Bouyer, Nicolas Markey, Daniel Stan
• Format: Article
• Language: English
• Published: Open Publishing Association 2016-09-01
• Series: Electronic Proceedings in Theoretical Computer Science
• Online Access: http://arxiv.org/pdf/1609.04089v1

We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward objectives, and their existence is undecidable with qualitative reachability objectives (and only three players). However, these results rely on the fact that the players can enforce infinite plays while trying to improve their payoffs. In this paper, we introduce a relaxed notion of equilibria, where deviations are imprecise. We prove that contrary to Nash equilibria, such (stationary) equilibria always exist, and we develop a PSPACE algorithm to compute one.