IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2503.17387.html
   My bibliography  Save this paper

On Nash Equilibria in Play-Once and Terminal Deterministic Graphical Games

Author

Listed:
  • Endre Boros
  • Vladimir Gurvich
  • Kazuhisa Makino

Abstract

We consider finite $n$-person deterministic graphical games and study the existence of pure stationary Nash-equilibrium in such games. We assume that all infinite plays are equivalent and form a unique outcome, while each terminal position is a separate outcome. It is known that for $n=2$ such a game always has a Nash equilibrium, while that may not be true for $n > 2$. A game is called {\em play-once} if each player controls a unique position and {\em terminal} if any terminal outcome is better than the infinite one for each player. We prove in this paper that play-once games have Nash equilibria. We also show that terminal games have Nash equilibria if they have at most three terminals.

Suggested Citation

  • Endre Boros & Vladimir Gurvich & Kazuhisa Makino, 2025. "On Nash Equilibria in Play-Once and Terminal Deterministic Graphical Games," Papers 2503.17387, arXiv.org.
  • Handle: RePEc:arx:papers:2503.17387
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2503.17387
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Boros, E. & Gurvich, V., 2003. "On Nash-solvability in pure stationary strategies of finite games with perfect information which may have cycles," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 207-241, October.
    2. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
    3. Endre Boros & Paolo Giulio Franciosa & Vladimir Gurvich & Michael Vyalyi, 2024. "Deterministic n-person shortest path and terminal games on symmetric digraphs have Nash equilibria in pure stationary strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 449-473, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nikolai Kukushkin, 2011. "Acyclicity of improvements in finite game forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 147-177, February.
    2. Di Feng & Bettina Klaus, 2022. "Preference revelation games and strict cores of multiple‐type housing market problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 61-76, March.
    3. Mark Voorneveld & Peter Borm & Freek Van Megen & Stef Tijs & Giovanni Facchini, 1999. "Congestion Games And Potentials Reconsidered," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 283-299.
    4. Arnold, Tone & Wooders, Myrna, 2002. "Dynamic Club Formation with Coordination," Economic Research Papers 269414, University of Warwick - Department of Economics.
    5. Ryo Kawasaki & Hideo Konishi & Junki Yukawa, 2023. "Equilibria in bottleneck games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 649-685, September.
    6. Xujin Chen & Zhuo Diao & Xiaodong Hu, 2022. "On weak Pareto optimality of nonatomic routing networks," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1705-1723, October.
    7. Aner Sela & Ishay Rabi & Chen Cohen, 2023. "An Algorithmic Analysis of Parallel Contests," Working Papers 2317, Ben-Gurion University of the Negev, Department of Economics.
    8. Le Breton, Michel & Shapoval, Alexander & Weber, Shlomo, 2021. "A game-theoretical model of the landscape theory," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 41-46.
    9. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    10. Zhan Wang & Jinpeng Ma & Hongwei Zhang, 2023. "Object-based unawareness: Theory and applications," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 8(1), pages 1-55, December.
    11. Samir Sbabou & Hatem Smaoui & Abderrahmane Ziad, 2013. "A formula for Nash equilibria in monotone singleton congestion games," Economics Bulletin, AccessEcon, vol. 33(1), pages 334-339.
    12. Abderrahmane ZIAD & Samir SBABOU & Hatem SMAOUI, CEMOI, 2011. "Nonsymmetric singleton congestion games: case of two resources," Economics Working Paper Archive (University of Rennes & University of Caen) 201113, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    13. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    14. Holzman, Ron & Law-yone (Lev-tov), Nissan, 2003. "Network structure and strong equilibrium in route selection games," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 193-205, October.
    15. György Dósa & Leah Epstein, 2019. "Pareto optimal equilibria for selfish bin packing with uniform cost sharing," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 827-847, April.
    16. Marco Scarsini & Tristan Tomala, 2012. "Repeated congestion games with bounded rationality," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 651-669, August.
    17. Epstein, Amir & Feldman, Michal & Mansour, Yishay, 2009. "Strong equilibrium in cost sharing connection games," Games and Economic Behavior, Elsevier, vol. 67(1), pages 51-68, September.
    18. Xujin Chen & Zhuo Diao & Xiaodong Hu, 0. "On weak Pareto optimality of nonatomic routing networks," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-19.
    19. Igal Milchtaich, 2015. "Network topology and equilibrium existence in weighted network congestion games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 515-541, August.
    20. Epstein, Amir & Feldman, Michal & Mansour, Yishay, 2009. "Efficient graph topologies in network routing games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 115-125, May.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2503.17387. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.