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The Complexity of SPEs in Mean-Payoff Games

Authors Léonard Brice, Jean-François Raskin, Marie van den Bogaard



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Author Details

Léonard Brice
  • Université libre de Bruxelles, Brussels, Belgium
Jean-François Raskin
  • Université libre de Bruxelles, Brussels, Belgium
Marie van den Bogaard
  • Univ Gustave Eiffel, CNRS, LIGM, F-77454 Marne-la-Vallée, France

Acknowledgements

We wish to thank the anonymous reviewers for their useful comments, in particular for the question that led us to add Lemma 1 to this paper.

Cite AsGet BibTex

Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. The Complexity of SPEs in Mean-Payoff Games. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 116:1-116:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ICALP.2022.116

Abstract

We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst case complexity was left open.

Subject Classification

ACM Subject Classification
  • Software and its engineering → Formal methods
  • Theory of computation → Logic and verification
  • Theory of computation → Solution concepts in game theory
Keywords
  • Games on graphs
  • subgame-perfect equilibria
  • mean-payoff objectives

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References

  1. Romain Brenguier, Lorenzo Clemente, Paul Hunter, Guillermo A. Pérez, Mickael Randour, Jean-François Raskin, Ocan Sankur, and Mathieu Sassolas. Non-zero sum games for reactive synthesis. In Language and Automata Theory and Applications - 10th International Conference, LATA 2016, Prague, Czech Republic, March 14-18, 2016, Proceedings, volume 9618 of Lecture Notes in Computer Science, pages 3-23. Springer, 2016. Google Scholar
  2. Romain Brenguier and Jean-François Raskin. Pareto curves of multidimensional mean-payoff games. In Daniel Kroening and Corina S. Pasareanu, editors, Computer Aided Verification - 27th International Conference, CAV 2015, San Francisco, CA, USA, July 18-24, 2015, Proceedings, Part II, volume 9207 of Lecture Notes in Computer Science, pages 251-267. Springer, 2015. Google Scholar
  3. Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. Subgame-perfect equilibria in mean-payoff games. In Serge Haddad and Daniele Varacca, editors, 32nd International Conference on Concurrency Theory, CONCUR 2021, August 24-27, 2021, Virtual Conference, volume 203 of LIPIcs, pages 8:1-8:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.CONCUR.2021.8.
  4. Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. The complexity of spes in mean-payoff games. CoRR, abs/2202.08499, 2022. URL: http://arxiv.org/abs/2202.08499.
  5. Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. On the complexity of spes in parity games. In Florin Manea and Alex Simpson, editors, 30th EACSL Annual Conference on Computer Science Logic, CSL 2022, February 14-19, 2022, Göttingen, Germany (Virtual Conference), volume 216 of LIPIcs, pages 10:1-10:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.CSL.2022.10.
  6. Thomas Brihaye, Véronique Bruyère, Aline Goeminne, Jean-François Raskin, and Marie van den Bogaard. The complexity of subgame perfect equilibria in quantitative reachability games. In CONCUR, volume 140 of LIPIcs, pages 13:1-13:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. Google Scholar
  7. Thomas Brihaye, Véronique Bruyère, Noémie Meunier, and Jean-François Raskin. Weak subgame perfect equilibria and their application to quantitative reachability. In 24th EACSL Annual Conference on Computer Science Logic, CSL 2015, September 7-10, 2015, Berlin, Germany, volume 41 of LIPIcs, pages 504-518. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. Google Scholar
  8. Thomas Brihaye, Julie De Pril, and Sven Schewe. Multiplayer cost games with simple nash equilibria. In Logical Foundations of Computer Science, International Symposium, LFCS 2013, San Diego, CA, USA, January 6-8, 2013. Proceedings, volume 7734 of Lecture Notes in Computer Science, pages 59-73. Springer, 2013. Google Scholar
  9. Véronique Bruyère. Computer aided synthesis: A game-theoretic approach. In Developments in Language Theory - 21st International Conference, DLT 2017, Liège, Belgium, August 7-11, 2017, Proceedings, volume 10396 of Lecture Notes in Computer Science, pages 3-35. Springer, 2017. Google Scholar
  10. Véronique Bruyère. Synthesis of equilibria in infinite-duration games on graphs. ACM SIGLOG News, 8(2):4-29, 2021. Google Scholar
  11. Véronique Bruyère, Stéphane Le Roux, Arno Pauly, and Jean-François Raskin. On the existence of weak subgame perfect equilibria. In Foundations of Software Science and Computation Structures - 20th International Conference, FOSSACS 2017, Uppsala, Sweden, April 22-29, 2017, Proceedings, volume 10203 of Lecture Notes in Computer Science, pages 145-161, 2017. Google Scholar
  12. Krishnendu Chatterjee. Concurrent games with tail objectives. Theor. Comput. Sci., 388(1-3):181-198, 2007. Google Scholar
  13. Krishnendu Chatterjee, Laurent Doyen, Herbert Edelsbrunner, Thomas A. Henzinger, and Philippe Rannou. Mean-payoff automaton expressions. In Paul Gastin and François Laroussinie, editors, CONCUR 2010 - Concurrency Theory, 21th International Conference, CONCUR 2010, Paris, France, August 31-September 3, 2010. Proceedings, volume 6269 of Lecture Notes in Computer Science, pages 269-283. Springer, 2010. Google Scholar
  14. Dana Fisman, Orna Kupferman, and Yoad Lustig. Rational synthesis. In Javier Esparza and Rupak Majumdar, editors, Tools and Algorithms for the Construction and Analysis of Systems, 16th International Conference, TACAS 2010, Paphos, Cyprus, March 20-28, 2010. Proceedings, volume 6015 of Lecture Notes in Computer Science, pages 190-204. Springer, 2010. Google Scholar
  15. János Flesch and Arkadi Predtetchinski. A characterization of subgame-perfect equilibrium plays in borel games of perfect information. Math. Oper. Res., 42(4):1162-1179, 2017. Google Scholar
  16. Erich Grädel and Michael Ummels. Solution Concepts and Algorithms for Infinite Multiplayer Games. In Krzysztof Apt and Robert van Rooij, editors, New Perspectives on Games and Interaction, volume 4 of Texts in Logic and Games, pages 151-178. Amsterdam University Press, 2008. Google Scholar
  17. Richard M. Karp. A characterization of the minimum cycle mean in a digraph. Discret. Math., 23(3):309-311, 1978. Google Scholar
  18. Eryk Kopczynski. Half-positional determinacy of infinite games. In Michele Bugliesi, Bart Preneel, Vladimiro Sassone, and Ingo Wegener, editors, Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Venice, Italy, July 10-14, 2006, Proceedings, Part II, volume 4052 of Lecture Notes in Computer Science, pages 336-347. Springer, 2006. Google Scholar
  19. Orna Kupferman, Giuseppe Perelli, and Moshe Y. Vardi. Synthesis with rational environments. Ann. Math. Artif. Intell., 78(1):3-20, 2016. Google Scholar
  20. Donald A. Martin. Borel determinacy. Annals of Mathematics, pages 363-371, 1975. Google Scholar
  21. Noémie Meunier. Multi-Player Quantitative Games: Equilibria and Algorithms. PhD thesis, Université de Mons, 2016. Google Scholar
  22. Martin J. Osborne. An introduction to game theory. Oxford Univ. Press, 2004. Google Scholar
  23. Eilon Solan and Nicolas Vieille. Deterministic multi-player dynkin games. Journal of Mathematical Economics, 39(8):911-929, 2003. Google Scholar
  24. Yaron Velner, Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger, Alexander Moshe Rabinovich, and Jean-François Raskin. The complexity of multi-mean-payoff and multi-energy games. Inf. Comput., 241:177-196, 2015. Google Scholar
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