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Reducing Stochastic Games to Semidefinite Programming

Authors Manuel Bodirsky , Georg Loho , Mateusz Skomra

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ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Semidefinite programming
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Mean-payoff games
  • stochastic games
  • semidefinite programming
  • max-average constraints
  • max-atom problem

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Abstract

We present a polynomial-time reduction from max-average constraints to the feasibility problem for semidefinite programs. This shows that Condon’s simple stochastic games, stochastic mean payoff games, and in particular mean payoff games and parity games can all be reduced to semidefinite programming.

Cite As Get BibTex

Manuel Bodirsky, Georg Loho, and Mateusz Skomra. Reducing Stochastic Games to Semidefinite Programming. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 145:1-145:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.145

Author Details

Manuel Bodirsky
  • Institut für Algebra, TU Dresden, Germany
Georg Loho
  • FU Berlin, Germany
  • U Twente, The Netherlands
Mateusz Skomra
  • LAAS-CNRS, Université de Toulouse, CNRS, Toulouse, France

Funding

This research benefited from the support of the FMJH Program PGMO.
  • Bodirsky, Manuel: The author received funding from the ERC (Grant Agreement no. 101071674, POCOCOP). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency.
  • Skomra, Mateusz: The author has been supported by European Union’s HORIZON–MSCA-2023-DN-JD programme under the Horizon Europe (HORIZON) Marie Skłodowska-Curie Actions, grant agreement 101120296 (TENORS).

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