Fragility and Robustness in Mean-Payoff Adversarial Stackelberg Games

Authors Mrudula Balachander, Shibashis Guha, Jean-François Raskin

Thumbnail PDF


  • Filesize: 0.76 MB
  • 17 pages

Document Identifiers

Author Details

Mrudula Balachander
  • Université libre de Bruxelles, Brussels, Belgium
Shibashis Guha
  • Tata Institute of Fundamental Research, Mumbai, India
Jean-François Raskin
  • Université libre de Bruxelles, Brussels, Belgium

Cite AsGet BibTex

Mrudula Balachander, Shibashis Guha, and Jean-François Raskin. Fragility and Robustness in Mean-Payoff Adversarial Stackelberg Games. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Two-player mean-payoff Stackelberg games are nonzero-sum infinite duration games played on a bi-weighted graph by Leader (Player 0) and Follower (Player 1). Such games are played sequentially: first, Leader announces her strategy, second, Follower chooses his best-response. If we cannot impose which best-response is chosen by Follower, we say that Follower, though strategic, is adversarial towards Leader. The maximal value that Leader can get in this nonzero-sum game is called the adversarial Stackelberg value (ASV) of the game. We study the robustness of strategies for Leader in these games against two types of deviations: (i) Modeling imprecision - the weights on the edges of the game arena may not be exactly correct, they may be delta-away from the right one. (ii) Sub-optimal response - Follower may play epsilon-optimal best-responses instead of perfect best-responses. First, we show that if the game is zero-sum then robustness is guaranteed while in the nonzero-sum case, optimal strategies for ASV are fragile. Second, we provide a solution concept to obtain strategies for Leader that are robust to both modeling imprecision, and as well as to the epsilon-optimal responses of Follower, and study several properties and algorithmic problems related to this solution concept.

Subject Classification

ACM Subject Classification
  • Theory of computation → Solution concepts in game theory
  • Theory of computation → Mathematical optimization
  • Theory of computation → Logic and verification
  • mean-payoff
  • Stackelberg games
  • synthesis


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Mrudula Balachander, Shibashis Guha, and Jean-François Raskin. Fragility and robustness in mean-payoff adversarial stackelberg games. CoRR, abs/2007.07209, 2020. URL:
  2. Roderick Bloem, Krishnendu Chatterjee, Karin Greimel, Thomas A. Henzinger, Georg Hofferek, Barbara Jobstmann, Bettina Könighofer, and Robert Könighofer. Synthesizing robust systems. Acta Informatica, 51(3-4):193-220, 2014. Google Scholar
  3. 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, pages 3-23, 2016. Google Scholar
  4. Véronique Bruyère, Noémie Meunier, and Jean-François Raskin. Secure equilibria in weighted games. In Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS '14, Vienna, Austria, July 14-18, 2014, pages 26:1-26:26. ACM, 2014. Google Scholar
  5. Krishnendu Chatterjee, Laurent Doyen, Herbert Edelsbrunner, Thomas A. Henzinger, and Philippe Rannou. Mean-payoff automaton expressions. In CONCUR 2010 - Concurrency Theory, 21th International Conference, Paris, France, August 31-September 3, 2010. Proceedings, pages 269-283, 2010. Google Scholar
  6. Krishnendu Chatterjee, Thomas A. Henzinger, and Marcin Jurdzinski. Games with secure equilibria. Theor. Comput. Sci., 365(1-2):67-82, 2006. Google Scholar
  7. 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, pages 121:1-121:15, 2016. Google Scholar
  8. Emmanuel Filiot, Raffaella Gentilini, and Jean-François Raskin. The adversarial stackelberg value in quantitative games. In 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference), pages 127:1-127:18, 2020. Google Scholar
  9. 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, pages 190-204, 2010. Google Scholar
  10. Anshul Gupta and Sven Schewe. Quantitative verification in rational environments. In 21st International Symposium on Temporal Representation and Reasoning, TIME 2014, Verona, Italy, September 8-10, 2014, pages 123-131, 2014. Google Scholar
  11. Anshul Gupta and Sven Schewe. Buying optimal payoffs in bi-matrix games. Games, 9(3):40, 2018. Google Scholar
  12. Anshul Gupta, Sven Schewe, Ashutosh Trivedi, Maram Sai Krishna Deepak, and Bharath Kumar Padarthi. Incentive stackelberg mean-payoff games. In Software Engineering and Formal Methods - 14th International Conference, SEFM 2016, Held as Part of STAF 2016, Vienna, Austria, July 4-8, 2016, Proceedings, pages 304-320, 2016. Google Scholar
  13. Anshul Gupta, Sven Schewe, and Dominik Wojtczak. Making the best of limited memory in multi-player discounted sum games. In Proceedings Sixth International Symposium on Games, Automata, Logics and Formal Verification, GandALF 2015, Genoa, Italy, 21-22nd September 2015, pages 16-30, 2015. Google Scholar
  14. Orna Kupferman, Giuseppe Perelli, and Moshe Y. Vardi. Synthesis with rational environments. Ann. Math. Artif. Intell., 78(1):3-20, 2016. Google Scholar
  15. Amir Pnueli and Roni Rosner. On the synthesis of a reactive module. In Conference Record of the Sixteenth Annual ACM Symposium on Principles of Programming Languages, Austin, Texas, USA, January 11-13, 1989, pages 179-190, 1989. Google Scholar
  16. Heinrich Freiherr von Stackelberg. Marktform und Gleichgewicht. Wien und Berlin, J. Springer, 1934. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail