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Mean-Payoff and Energy Discrete-Bidding Games

Authors Guy Avni , Suman Sadhukhan

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Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
  • Theory of computation → Formal languages and automata theory
Keywords
  • Bidding games
  • Discrete-bidding
  • Mean-payoff games
  • energy games

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Abstract

A bidding game is played on a graph as follows. A token is placed on an initial vertex and both players are allocated budgets. In each turn, the players simultaneously submit bids that do not exceed their available budgets, the higher bidder moves the token, and pays the bid to the lower bidder. We focus on discrete-bidding, which are motivated by practical applications and restrict the granularity of the players' bids, e.g, bids must be given in cents. We study, for the first time, discrete-bidding games with mean-payoff and energy objectives. In contrast, mean-payoff continuous-bidding games (i.e., no granularity restrictions) are understood and exhibit a rich mathematical structure. The threshold budget is a necessary and sufficient initial budget for winning an energy game or guaranteeing a target payoff in a mean-payoff game. We first establish existence of threshold budgets; a non-trivial property due to the concurrent moves of the players. Moreover, we identify the structure of the thresholds, which is key in obtaining compact strategies, and in turn, showing that finding threshold is in NP and coNP even in succinctly-represented games.

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Guy Avni and Suman Sadhukhan. Mean-Payoff and Energy Discrete-Bidding Games. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CSL.2026.32

Author Details

Guy Avni
  • Department of Computer Science, University of Haifa, Israel
Suman Sadhukhan
  • Department of Computer Science, University of Haifa, Israel

Funding

This research was supported in part by ISF grant no. 1679/21.

References

  1. M. Aghajohari, G. Avni, and T. A. Henzinger. Determinacy in discrete-bidding infinite-duration games. Log. Methods Comput. Sci., 17(1), 2021. URL: https://lmcs.episciences.org/7148.
  2. R. Alur, T. A. Henzinger, and O. Kupferman. Alternating-time temporal logic. J. ACM, 49(5):672-713, 2002. URL: https://doi.org/10.1145/585265.585270.
  3. G. Amanatidis, G. Birmpas, A. Filos-Ratsikas, and A. A. Voudouris. Fair division of indivisible goods: A survey. In Luc De Raedt, editor, Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI 2022, Vienna, Austria, 23-29 July 2022, pages 5385-5393. ijcai.org, 2022. URL: https://doi.org/10.24963/ijcai.2022/756.
  4. G. Avni, E. Kafshdar Goharshady, T. A. Henzinger, and K. Mallik. Bidding games with charging. In Rupak Majumdar and Alexandra Silva, editors, 35th International Conference on Concurrency Theory, CONCUR 2024, Calgary, Canada, September 9-13, 2024, volume 311 of LIPIcs, pages 8:1-8:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPIcs.CONCUR.2024.8.
  5. G. Avni, T. A. Henzinger, and V. Chonev. Infinite-duration bidding games. J. ACM, 66(4):31:1-31:29, 2019. URL: https://doi.org/10.1145/3340295.
  6. G. Avni, T. A. Henzinger, and R. Ibsen-Jensen. Infinite-duration poorman-bidding games. In George Christodoulou and Tobias Harks, editors, Web and Internet Economics - 14th International Conference, WINE 2018, Oxford, UK, December 15-17, 2018, Proceedings, volume 11316 of Lecture Notes in Computer Science, pages 21-36. Springer, 2018. URL: https://doi.org/10.1007/978-3-030-04612-5_2.
  7. G. Avni, T. A. Henzinger, and D. Zikelic. Bidding mechanisms in graph games. J. Comput. Syst. Sci., 119:133-144, 2021. URL: https://doi.org/10.1016/j.jcss.2021.02.008.
  8. G. Avni, I. Jecker, and Đ. Žikelić. Infinite-duration all-pay bidding games. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, Virtual Conference, January 10 - 13, 2021, pages 617-636. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976465.38.
  9. G. Avni, I. Jecker, and D. Zikelic. Bidding graph games with partially-observable budgets. In Brian Williams, Yiling Chen, and Jennifer Neville, editors, Thirty-Seventh AAAI Conference on Artificial Intelligence, AAAI 2023, Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence, IAAI 2023, Thirteenth Symposium on Educational Advances in Artificial Intelligence, EAAI 2023, Washington, DC, USA, February 7-14, 2023, pages 5464-5471. AAAI Press, 2023. URL: https://doi.org/10.1609/aaai.v37i5.25679.
  10. G. Avni, M. Kurecka, K. Mallik, P. Novotný, and S. Sadhukhan. Bidding games on markov decision processes with quantitative reachability objectives. In Proceedings of the 24th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2025, Detroit, MI, USA, May 19-23, 2025, pages 161-169. International Foundation for Autonomous Agents and Multiagent Systems / ACM, 2025. URL: https://doi.org/10.5555/3709347.3743528.
  11. G. Avni, K. Mallik, and S. Sadhukhan. Auction-based scheduling. In Bernd Finkbeiner and Laura Kovács, editors, Tools and Algorithms for the Construction and Analysis of Systems - 30th International Conference, TACAS 2024, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2024, Luxembourg City, Luxembourg, April 6-11, 2024, Proceedings, Part III, volume 14572 of Lecture Notes in Computer Science, pages 153-172. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-57256-2_8.
  12. G. Avni and S. Sadhukhan. Computing threshold budgets in discrete-bidding games. TheoretiCS, 4, 2025. URL: https://doi.org/10.46298/theoretics.25.5.
  13. Guy Avni and Suman Sadhukhan. Mean-payoff and energy discrete bidding games. CoRR, abs/2509.00506, 2025. URL: https://doi.org/10.48550/arXiv.2509.00506.
  14. H. Aziz, B. Li, He. Moulin, and X. Wu. Algorithmic fair allocation of indivisible items: a survey and new questions. SIGecom Exch., 20(1):24-40, 2022. URL: https://doi.org/10.1145/3572885.3572887.
  15. M. Babaioff, T. Ezra, and U. Feige. Fair-share allocations for agents with arbitrary entitlements. In Péter Biró, Shuchi Chawla, and Federico Echenique, editors, EC '21: The 22nd ACM Conference on Economics and Computation, Budapest, Hungary, July 18-23, 2021, page 127. ACM, 2021. URL: https://doi.org/10.1145/3465456.3467559.
  16. B. Bordais, P. Bouyer, and S. Le Roux. From local to global determinacy in concurrent graph games. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2021, Virtual Conference, December 15-17, 2021, volume 213 of LIPIcs, pages 41:1-41:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.FSTTCS.2021.41.
  17. P. Bouyer, U. Fahrenberg, K. Guldstrand Larsen, N. Markey, and J. Srba. Infinite runs in weighted timed automata with energy constraints. In Franck Cassez and Claude Jard, editors, Formal Modeling and Analysis of Timed Systems, 6th International Conference, FORMATS 2008, Saint Malo, France, September 15-17, 2008. Proceedings, volume 5215 of Lecture Notes in Computer Science, pages 33-47. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-85778-5_4.
  18. L. Brim, J. Chaloupka, L. Doyen, R. Gentilini, and J.-F. Raskin. Faster algorithms for mean-payoff games. Formal Methods Syst. Des., 38(2):97-118, 2011. URL: https://doi.org/10.1007/s10703-010-0105-x.
  19. A. Condon. The complexity of stochastic games. Inf. Comput., 96(2):203-224, 1992. URL: https://doi.org/10.1016/0890-5401(92)90048-K.
  20. M. Develin and S. Payne. Discrete bidding games. Electron. J. Comb., 17(1):R85, 2010. URL: https://doi.org/10.37236/357.
  21. A. Gorokh, S. Banerjee, and K. Iyer. The remarkable robustness of the repeated fisher market. In EC '21: The 22nd ACM Conference on Economics and Computation, Budapest, Hungary, July 18-23, 2021, page 562. ACM, 2021. URL: https://doi.org/10.1145/3465456.3467560.
  22. A. J. Lazarus, D. E. Loeb, J. G. Propp, W. R. Stromquist, and D. H. Ullman. Combinatorial games under auction play. Games and Economic Behavior, 27(2):229-264, 1999. URL: https://doi.org/10.1006/game.1998.0676.
  23. A. J. Lazarus, D. E. Loeb, J. G. Propp, and D. Ullman. Richman games. Games of No Chance, 29:439-449, 1996. URL: https://doi.org/10.1017/9781009701839.037.
  24. R. Meir, G. Kalai, and M. Tennenholtz. Bidding games and efficient allocations. Games Econ. Behav., 112:166-193, 2018. URL: https://doi.org/10.1016/j.geb.2018.08.005.
  25. S. Muthukrishnan. Ad exchanges: Research issues. In Stefano Leonardi, editor, Internet and Network Economics, 5th International Workshop, WINE 2009, Rome, Italy, December 14-18, 2009. Proceedings, volume 5929 of Lecture Notes in Computer Science, pages 1-12. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-10841-9_1.
  26. Y. Peres, O. Schramm, S. Sheffield, and D. B. Wilson. Tug-of-war and the infinity laplacian. J. Amer. Math. Soc., 22:167-210, 2009. URL: https://www.jstor.org/stable/40587228.
  27. A. Pnueli and R. 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. ACM Press, 1989. URL: https://doi.org/10.1145/75277.75293.
  28. M.O. Rabin. Decidability of second order theories and automata on infinite trees. Transaction of the AMS, 141:1-35, 1969. URL: https://doi.org/10.2307/1995086.
  29. U. Zwick and M. Paterson. The complexity of mean payoff games on graphs. Theor. Comput. Sci., 158(1&2):343-359, 1996. URL: https://doi.org/10.1016/0304-3975(95)00188-3.
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