Existential Theory of the Reals Completeness of Stationary Nash Equilibria in Perfect Information Stochastic Games
Kristoffer Arnsfelt Hansen,
Steffan Christ Sølvsten
Abstract:We show that the problem of deciding whether in a multi-player perfect information recursive game (i.e. a stochastic game with terminal rewards) there exists a stationary Nash equilibrium ensuring each player a certain payoff is ∃R-complete. Our result holds for acyclic games, where a Nash equilibrium may be computed efficiently by backward induction, and even for deterministic acyclic games with non-negative terminal rewards. We further extend our results to the existence of Nash equilibria where a single pla… Show more
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