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Beyond Admissibility: Dominance Between Chains of Strategies

Authors Nicolas Basset, Ismaël Jecker, Arno Pauly , Jean-François Raskin, Marie Van den Bogaard

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Author Details

Nicolas Basset
  • Université Grenoble Alpes, Grenoble, France
Ismaël Jecker
  • Department of Computer Science, Université Libre de Bruxelles, Brussels, Belgium
Arno Pauly
  • Department of Computer Science, Swansea University, Swansea, UK
Jean-François Raskin
  • Department of Computer Science, Université Libre de Bruxelles, Brussels, Belgium
Marie Van den Bogaard
  • Department of Computer Science, Université Libre de Bruxelles, Brussels, Belgium

Funding

This work was partially supported by the ERC inVEST (279499), the ARC project "Non-Zero Sum Game Graphs: Applications to Reactive Synthesis and Beyond" (Fédération Wallonie-Bruxelles), the EOS project "Verifying Learning Artificial Intelligence Systems" (FNRS-FWO), and the Belgian FNRS PDR project "Subgame perfection in graph games" (T.0088.18). J.-F. Raskin is Professeur Francqui de Recherche funded by the Francqui foundation.

Cite AsGet BibTex

Nicolas Basset, Ismaël Jecker, Arno Pauly, Jean-François Raskin, and Marie Van den Bogaard. Beyond Admissibility: Dominance Between Chains of Strategies. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CSL.2018.10

Abstract

Admissible strategies, i.e. those that are not dominated by any other strategy, are a typical rationality notion in game theory. In many classes of games this is justified by results showing that any strategy is admissible or dominated by an admissible strategy. However, in games played on finite graphs with quantitative objectives (as used for reactive synthesis), this is not the case. We consider increasing chains of strategies instead to recover a satisfactory rationality notion based on dominance in such games. We start with some order-theoretic considerations establishing sufficient criteria for this to work. We then turn our attention to generalised safety/reachability games as a particular application. We propose the notion of maximal uniform chain as the desired dominance-based rationality concept in these games. Decidability of some fundamental questions about uniform chains is established.

Subject Classification

ACM Subject Classification
  • Theory of computation → Solution concepts in game theory
  • Theory of computation → Automata extensions
Keywords
  • dominated strategies
  • admissible strategies
  • games played on finite graphs
  • reactive synthesis
  • reachability games
  • safety games
  • cofinal
  • order theory

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References

  1. Martín Abadi, Leslie Lamport, and Pierre Wolper. Realizable and unrealizable specifications of reactive systems. In ICALP'89, volume 372 of LNCS. Springer, 1989. Google Scholar
  2. Nicolas Basset, Gilles Geeraerts, Jean-François Raskin, and Ocan Sankur. Admissiblity in concurrent games. In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, volume 80 of LIPIcs, pages 123:1-123:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2017.123.
  3. Nicolas Basset, Ismaël Jecker, Arno Pauly, Jean-François Raskin, and Marie Van den Boogard. Beyond admissibility: Dominance between chains of strategies. arXiv 1805.11608, 2018. URL: https://arxiv.org/abs/1805.11608.
  4. Dietmar Berwanger. Admissibility in infinite games. In STACS 2007, 24th Annual Symposium on Theoretical Aspects of Computer Science, Aachen, Germany, February 22-24, 2007, Proceedings, pages 188-199, 2007. URL: http://dx.doi.org/10.1007/978-3-540-70918-3_17.
  5. Endre Boros, Khaled Elbassioni, Vladimir Gurvich, and Kazuhisa Makino. On Nash equilibria and improvement cycles in pure positional strategies for chess-like and backgammon-like n-person games. Discrete Mathematics, 312(4):772-788, 2012. URL: http://dx.doi.org/10.1016/j.disc.2011.11.011.
  6. Endre Boros, Vladimir Gurvich, and Emre Yamangil. Chess-like games may have no uniform nash equilibria even in mixed strategies. Game Theory, 2013. URL: http://dx.doi.org/10.1155/2013/534875.
  7. 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
  8. Romain Brenguier, Arno Pauly, Jean-François Raskin, and Ocan Sankur. Admissibility in Games with Imperfect Information (Invited Talk). In Roland Meyer and Uwe Nestmann, editors, 28th International Conference on Concurrency Theory (CONCUR 2017), volume 85 of LIPIcs, pages 2:1-2:23. Schloss Dagstuhl, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.CONCUR.2017.2.
  9. Romain Brenguier, Guillermo A. Pérez, Jean-François Raskin, and Ocan Sankur. Admissibility in quantitative graph games. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016, December 13-15, 2016, Chennai, India, pages 42:1-42:14, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2016.42.
  10. Romain Brenguier, Jean-François Raskin, and Ocan Sankur. Assume-admissible synthesis. Acta Inf., 54(1):41-83, 2017. Google Scholar
  11. Romain Brenguier, Jean-François Raskin, and Ocan Sankur. Assume-admissible synthesis. Acta Inf., 54(1):41-83, 2017. Google Scholar
  12. Romain Brenguier, Jean-François Raskin, and Mathieu Sassolas. The complexity of admissibility in omega-regular games. In CSL-LICS '14, 2014. ACM, 2014. URL: http://dx.doi.org/10.1145/2603088.2603143.
  13. Thomas Brihaye, Veroniqué Bruyère, and Julie De Pril. Equilibria in quantitative reachability games. In Proc. of CSR, volume 6072 of LNCS. Springer, 2010. URL: http://dx.doi.org/10.1007/978-3-642-13182-0_7.
  14. A. Ehrenfeucht and J. Mycielski. Positional strategies for mean payoff games. International Journal of Game Theory, 8(2):109-113, Jun 1979. URL: http://dx.doi.org/10.1007/BF01768705.
  15. Marco Faella. Admissible strategies in infinite games over graphs. In MFCS 2009, volume 5734 of Lecture Notes in Computer Science, pages 307-318. Springer, 2009. Google Scholar
  16. Deedlit (https://math.stackexchange.com/users deedlit). Height of a certain order. Mathematics Stack Exchange. URL:https://math.stackexchange.com/q/2436983 (version: 2017-09-20).
  17. Orna Kupferman. On high-quality synthesis. In S. Alexander Kulikov and J. Gerhard Woeginger, editors, 11th International Computer Science Symposium in Russia, CSR 2016, pages 1-15. Springer International Publishing, 2016. URL: http://dx.doi.org/10.1007/978-3-319-34171-2_1.
  18. Stéphane Le Roux and Arno Pauly. Extending finite memory determinacy. Information and Computation, 201X. URL: http://dx.doi.org/10.1016/j.ic.2018.02.024.
  19. George Markowsky. Chain-complete posets and directed sets with applications. Algebra Universalis, 6:53-68, 1976. URL: http://dx.doi.org/10.1007/BF02485815.
  20. Soumya Paul and Sunil Easaw Simon. Nash equilibrium in generalised muller games. In FSTTCS, volume 4 of LIPIcs, pages 335-346. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2009. Google Scholar
  21. Arno Pauly. The computational complexity of iterated elimination of dominated strategies. Theory of Computing Systems, pages 52-75, 2016. URL: http://dx.doi.org/10.1007/s00224-015-9637-1.
  22. Amir Pnueli and Roni Rosner. On the synthesis of a reactive module. In POPL, pages 179-190, 1989. URL: http://dx.doi.org/10.1145/75277.75293.
  23. H.J. Prömel, W. Thumser, and B. Voigt. Fast growing functions based on Ramsey theorems. Discrete Mathematics, 95(1):341-358, 1991. URL: http://dx.doi.org/0012-365X(91)90346-4.
  24. Stéphane Le Roux. From winning strategy to nash equilibrium. Math. Log. Q., 60(4-5):354-371, 2014. Google Scholar
  25. Wang Shang-Zhi and Li Bo-Yu. On the minimal cofinal subsets of a directed quasi-ordered set. Discrete Mathematics, 48(2):289-306, 1984. URL: http://dx.doi.org/10.1016/0012-365X(84)90189-4.
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