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arXiv · 2510.11550

On the Complexity of Stationary Nash Equilibria in Discounted Perfect Information Stochastic Games

Kristoffer Arnsfelt Hansen·Xinhao Nie
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Abstract

We study the problem of computing stationary Nash equilibria in discounted perfect information stochastic games from the viewpoint of computational complexity. For two-player games we prove the problem to be in PPAD, which together with a previous PPAD-hardness result precisely classifies the problem as PPAD-complete. In addition to this we give an improved and simpler PPAD-hardness proof for computing a stationary epsilon-Nash equilibrium. For 3-player games we construct games showing that rational-valued stationary Nash equilibria are not guaranteed to exist, and we use these to prove SqrtSum-hardness of computing a stationary Nash equilibrium in 4-player games.

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Kristoffer Arnsfelt Hansen, Xinhao Nie. 2025-10-13. On the Complexity of Stationary Nash Equilibria in Discounted Perfect Information Stochastic Games. https://arxiv.org/abs/2510.11550

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