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We study the existence of mixed-strategy equilibria in concurrent gamesplayed on graphs. While existence is guaranteed with safety objectives for eachplayer, Nash equilibria need not exist when players are given arbitraryterminal-reward objectives, and their existence is undecidable with qualitativereachability objectives (and only three players). However, these results relyon the fact that the players can enforce infinite plays while trying to improvetheir 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 tocompute one.

Stochastic Equilibria under Imprecise Deviations in Terminal-Reward Concurrent Games