Abstract
Ummels and Wojtczak initiated the study of finding Nash equilibria in simple stochastic multi-player games satisfying specific bounds. They showed that deciding the existence of pure-strategy Nash equilibria (pureNE) where a fixed player wins almost surely is undecidable for games with \(9\) players. They also showed that the problem remains undecidable for the finite-strategy Nash equilibrium (finNE) with \(14\) players. In this paper we improve their undecidability results by showing that pureNE and finNE problems remain undecidable for \(5\) or more players.
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The \(i\)th element of vector \(\bar{x}\) corresponds to the payoff of player \(i\).
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Das, A., Krishna, S.N., Manasa, L., Trivedi, A., Wojtczak, D. (2015). On Pure Nash Equilibria in Stochastic Games. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_31
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DOI: https://doi.org/10.1007/978-3-319-17142-5_31
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