2026-07-23T08:35:20Z https://drops.dagstuhl.de/oai

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The Complexity of Infinite-Horizon General-Sum Stochastic Games Jin, Yujia Muthukumar, Vidya Sidford, Aaron complexity stochastic games general-sum games Nash equilibrium We study the complexity of computing stationary Nash equilibrium (NE) in n-player infinite-horizon general-sum stochastic games. We focus on the problem of computing NE in such stochastic games when each player is restricted to choosing a stationary policy and rewards are discounted. First, we prove that computing such NE is in PPAD (in addition to clearly being PPAD-hard). Second, we consider turn-based specializations of such games where at each state there is at most a single player that can take actions and show that these (seemingly-simpler) games remain PPAD-hard. Third, we show that under further structural assumptions on the rewards computing NE in such turn-based games is possible in polynomial time. Towards achieving these results we establish structural facts about stochastic games of broader utility, including monotonicity of utilities under single-state single-action changes and reductions to settings where each player controls a single state. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yujia Jin and Vidya Muthukumar and Aaron Sidford 2023 Is Part Of LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2023.76 urn:nbn:de:0030-drops-175791 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.76 eng https://creativecommons.org/licenses/by/4.0/legalcode