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DOI: 10.4230/LIPIcs.ITCS.2023.76
The Complexity of Infinite-Horizon General-Sum Stochastic Games

Authors: Yujia Jin, Vidya Muthukumar, and Aaron Sidford

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
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.
Cite as

Yujia Jin, Vidya Muthukumar, and Aaron Sidford. The Complexity of Infinite-Horizon General-Sum Stochastic Games. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 76:1-76:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jin_et_al:LIPIcs.ITCS.2023.76,
  author =	{Jin, Yujia and Muthukumar, Vidya and Sidford, Aaron},
  title =	{{The Complexity of Infinite-Horizon General-Sum Stochastic Games}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{76:1--76:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.76},
  URN =		{urn:nbn:de:0030-drops-175791},
  doi =		{10.4230/LIPIcs.ITCS.2023.76},
  annote =	{Keywords: complexity, stochastic games, general-sum games, Nash equilibrium}
}
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