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The Complexity of Rational Synthesis for Concurrent Games

Authors Rodica Condurache, Youssouf Oualhadj, Nicolas Troquard

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Author Details

Rodica Condurache
  • Computer Science Department, "A.I.Cuza" University, Iaşi, 700483, ROMANIA
Youssouf Oualhadj
  • Université Paris Est Créteil, LACL(EA 4219), UPEC, 94010 Créteil Cedex, France
Nicolas Troquard
  • The KRDB Research Centre, Free University of Bozen-Bolzano, I-39100 Bozen-Bolzano BZ, Italy

Cite AsGet BibTex

Rodica Condurache, Youssouf Oualhadj, and Nicolas Troquard. The Complexity of Rational Synthesis for Concurrent Games. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 38:1-38:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


In this paper, we investigate the rational synthesis problem for concurrent game structures for a variety of objectives ranging from reachability to Muller condition. We propose a new algorithm that establishes the decidability of the non cooperative rational synthesis problem that relies solely on game theoretic techniques as opposed to previous approaches that are logic based. Given an instance of the rational synthesis problem, we construct a zero-sum turn-based game that can be adapted to each one of the class of objectives. We obtain new complexity results. In particular, we show that in the cases of reachability, safety, Büchi, and co-Büchi objectives the problem is in PSpace, providing a tight upper-bound to the PSpace-hardness already established for turn-based games. In the case of Muller objective the problem is in ExpTime. We also obtain positive results when we assume a fixed number of agents, in which case the problem falls into PTime for reachability, safety, Büchi, and co-Büchi objectives.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Solution concepts in game theory
  • Synthesis
  • concurrent games
  • Nash equilibria


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  2. Patricia Bouyer, Romain Brenguier, Nicolas Markey, and Michael Ummels. Pure nash equilibria in concurrent deterministic games. Logical Methods in Computer Science, 11(2), 2015. URL:
  3. Rodica Condurache, Emmanuel Filiot, Raffaella Gentilini, and Jean-François Raskin. The complexity of rational synthesis. In 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy, volume 55 of LIPIcs, pages 121:1-121:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. URL:
  4. Dana Fisman, Orna Kupferman, and Yoad Lustig. Rational synthesis. In Tools and Algorithms for the Construction and Analysis of Systems, 16th International Conference, TACAS 2010, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2010, Paphos, Cyprus, March 20-28, 2010. Proceedings, volume 6015 of Lecture Notes in Computer Science, pages 190-204. Springer, 2010. URL:
  5. Marcin Jurdzinski, Mike Paterson, and Uri Zwick. A deterministic subexponential algorithm for solving parity games. In Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2006, Miami, Florida, USA, January 22-26, 2006, pages 117-123, 2006. URL:
  6. Orna Kupferman, Giuseppe Perelli, and Moshe Y. Vardi. Synthesis with rational environments. In Multi-Agent Systems - 12th European Conference, EUMAS 2014, Prague, Czech Republic, December 18-19, 2014, Revised Selected Papers, pages 219-235, 2014. URL:
  7. Orna Kupferman, Giuseppe Perelli, and Moshe Y. Vardi. Synthesis with rational environments. Ann. Math. Artif. Intell., 78(1):3-20, 2016. URL:
  8. Sven Schewe. Solving parity games in big steps. In FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science, 27th International Conference, New Delhi, India, December 12-14, 2007, Proceedings, volume 4855 of Lecture Notes in Computer Science, pages 449-460. Springer, 2007. URL:
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