On the Complexity of Stationary Nash Equilibria in Discounted Perfect Information Stochastic Games
Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hansen, Kristoffer Arnsfelt, Nie, Xinhao
Institution: Aarhus University
Language: English
Topic: Game Theory and Applications
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7091188130
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