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Bidding Games with Charging

Authors Guy Avni , Ehsan Kafshdar Goharshady , Thomas A. Henzinger , Kaushik Mallik

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Author Details

Guy Avni
  • University of Haifa, Israel
Ehsan Kafshdar Goharshady
  • Institute of Science and Technology Austria (ISTA), Austria
Thomas A. Henzinger
  • Institute of Science and Technology Austria (ISTA), Austria
Kaushik Mallik
  • Institute of Science and Technology Austria (ISTA), Austria

Funding

This work was supported in part by the ERC projects ERC-2020-AdG 101020093 and CoG 863818 (ForM-SMArt) and by ISF grant no. 1679/21.

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Guy Avni, Ehsan Kafshdar Goharshady, Thomas A. Henzinger, and Kaushik Mallik. Bidding Games with Charging. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CONCUR.2024.8

Abstract

Graph games lie at the algorithmic core of many automated design problems in computer science. These are games usually played between two players on a given graph, where the players keep moving a token along the edges according to pre-determined rules (turn-based, concurrent, etc.), and the winner is decided based on the infinite path (aka play) traversed by the token from a given initial position. In bidding games, the players initially get some monetary budgets which they need to use to bid for the privilege of moving the token at each step. Each round of bidding affects the players' available budgets, which is the only form of update that the budgets experience. We introduce bidding games with charging where the players can additionally improve their budgets during the game by collecting vertex-dependent monetary rewards, aka the "charges." Unlike traditional bidding games (where all charges are zero), bidding games with charging allow non-trivial recurrent behaviors. For example, a reachability objective may require multiple detours to vertices with high charges to earn additional budget. We show that, nonetheless, the central property of traditional bidding games generalizes to bidding games with charging: For each vertex there exists a threshold ratio, which is the necessary and sufficient fraction of the total budget for winning the game from that vertex. While the thresholds of traditional bidding games correspond to unique fixed points of linear systems of equations, in games with charging, these fixed points are no longer unique. This significantly complicates the proof of existence and the algorithmic computation of thresholds for infinite-duration objectives. We also provide the lower complexity bounds for computing thresholds for Rabin and Streett objectives, which are the first known lower bounds in any form of bidding games (with or without charging), and we solve the following repair problem for safety and reachability games that have unsatisfiable objectives: Can we distribute a given amount of charge to the players in a way such that the objective can be satisfied?

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • Bidding games on graphs
  • ω-regular objectives

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References

  1. M. Aghajohari, G. Avni, and T. A. Henzinger. Determinacy in discrete-bidding infinite-duration games. Log. Methods Comput. Sci., 17(1), 2021. Google Scholar
  2. R. Alur, T. A. Henzinger, and O. Kupferman. Alternating-time temporal logic. J. ACM, 49(5):672-713, 2002. Google Scholar
  3. G. Avni, T. A. Henzinger, and V. Chonev. Infinite-duration bidding games. In Proc. 28th CONCUR, volume 85 of LIPIcs, pages 21:1-21:18, 2017. Google Scholar
  4. G. Avni, T. A. Henzinger, and V. Chonev. Infinite-duration bidding games. J. ACM, 66(4):31:1-31:29, 2019. Google Scholar
  5. G. Avni, T. A. Henzinger, and R. Ibsen-Jensen. Infinite-duration poorman-bidding games. In Proc. 14th WINE, volume 11316 of LNCS, pages 21-36. Springer, 2018. Google Scholar
  6. G. Avni, T. A. Henzinger, and Đ. Žikelić. Bidding mechanisms in graph games. In Proc. 44th MFCS, volume 138 of LIPIcs, pages 11:1-11:13, 2019. Google Scholar
  7. G. Avni, T. A. Henzinger, and D. Zikelic. Bidding mechanisms in graph games. J. Comput. Syst. Sci., 119:133-144, 2021. Google Scholar
  8. G. Avni, R. Ibsen-Jensen, and J. Tkadlec. All-pay bidding games on graphs. In Proc. 34th AAAI, pages 1798-1805. AAAI Press, 2020. Google Scholar
  9. G. Avni, I. Jecker, and Đ. Žikelić. Infinite-duration all-pay bidding games. In Proc. 32nd SODA, pages 617-636, 2021. Google Scholar
  10. G. Avni, I. Jecker, and D. Zikelic. Bidding graph games with partially-observable budgets. In Proc. 37th AAAI, 2023. Google Scholar
  11. G. Avni, T. Meggendorfer, S. Sadhukhan, J. Tkadlec, and Ð. Zikelic. Reachability poorman discrete-bidding games. In Proc. 26th ECAI, volume 372 of Frontiers in Artificial Intelligence and Applications, pages 141-148. IOS Press, 2023. Google Scholar
  12. G. Avni and S. Sadhukhan. Computing threshold budgets in discrete-bidding games. In Proc. 42nd FSTTCS, volume 250 of LIPIcs, pages 30:1-30:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  13. Guy Avni, Ehsan Kafshdar Goharshady, Thomas A. Henzinger, and Kaushik Mallik. Bidding games with charging, 2024. URL: https://arxiv.org/abs/2407.06288.
  14. Guy Avni, Kaushik Mallik, and Suman Sadhukhan. Auction-based scheduling. In TACAS (3), volume 14572 of Lecture Notes in Computer Science, pages 153-172. Springer, 2024. Google Scholar
  15. František Blahoudek, Petr Novotnỳ, Melkior Ornik, Pranay Thangeda, and Ufuk Topcu. Efficient strategy synthesis for mdps with resource constraints. IEEE Transactions on Automatic Control, 2022. Google Scholar
  16. Patricia Bouyer, Uli Fahrenberg, Kim G Larsen, Nicolas Markey, and Jiří Srba. Infinite runs in weighted timed automata with energy constraints. In Formal Modeling and Analysis of Timed Systems: 6th International Conference, FORMATS 2008, Saint Malo, France, September 15-17, 2008. Proceedings 6, pages 33-47. Springer, 2008. Google Scholar
  17. Arindam Chakrabarti, Luca De Alfaro, Thomas A Henzinger, and Mariëlle Stoelinga. Resource interfaces. In International Workshop on Embedded Software, pages 117-133. Springer, 2003. Google Scholar
  18. A. Condon. The complexity of stochastic games. Inf. Comput., 96(2):203-224, 1992. Google Scholar
  19. M. Develin and S. Payne. Discrete bidding games. The Electronic Journal of Combinatorics, 17(1):R85, 2010. Google Scholar
  20. Robert G Jeroslow. The polynomial hierarchy and a simple model for competitive analysis. Mathematical programming, 32(2):146-164, 1985. Google Scholar
  21. 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. Google Scholar
  22. A. J. Lazarus, D. E. Loeb, J. G. Propp, and D. Ullman. Richman games. Games of No Chance, 29:439-449, 1996. Google Scholar
  23. R. Meir, G. Kalai, and M. Tennenholtz. Bidding games and efficient allocations. Games and Economic Behavior, 112:166-193, 2018. URL: https://doi.org/10.1016/j.geb.2018.08.005.
  24. 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. Google Scholar
  25. A. Pnueli and R. Rosner. On the synthesis of a reactive module. In Proc. 16th POPL, pages 179-190, 1989. Google Scholar
  26. M.O. Rabin. Decidability of second order theories and automata on infinite trees. Transaction of the AMS, 141:1-35, 1969. Google Scholar
  27. W. Zielonka. Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theor. Comput. Sci., 200(1-2):135-183, 1998. Google Scholar
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