IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v71y2021i2d10.1007_s00199-020-01260-6.html
   My bibliography  Save this article

Subgame perfection in recursive perfect information games

Author

Listed:
  • Jeroen Kuipers

    (Maastricht University)

  • János Flesch

    (Maastricht University)

  • Gijs Schoenmakers

    (Maastricht University)

  • Koos Vrieze

    (Maastricht University)

Abstract

We consider sequential multi-player games with perfect information and with deterministic transitions. The players receive a reward upon termination of the game, which depends on the state where the game was terminated. If the game does not terminate, then the rewards of the players are equal to zero. We prove that, for every game in this class, a subgame perfect $$\varepsilon $$ ε -equilibrium exists, for all $$\varepsilon > 0$$ ε > 0 . The proof is constructive and suggests a finite algorithm to calculate such an equilibrium.

Suggested Citation

  • Jeroen Kuipers & János Flesch & Gijs Schoenmakers & Koos Vrieze, 2021. "Subgame perfection in recursive perfect information games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 603-662, March.
    • Handle: RePEc:spr:joecth:v:71:y:2021:i:2:d:10.1007_s00199-020-01260-6
    DOI: 10.1007/s00199-020-01260-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-020-01260-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-020-01260-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ayala Mashiah-Yaakovi, 2014. "Subgame perfect equilibria in stopping games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 89-135, February.
    2. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    3. Carlos Alós-Ferrer & Klaus Ritzberger, 2016. "The Theory of Extensive Form Games," Springer Series in Game Theory, Springer, number 978-3-662-49944-3, July.
    4. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    5. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    6. J. Kuipers & J. Flesch & G. Schoenmakers & K. Vrieze, 2016. "Subgame-perfection in recursive perfect information games, where each player controls one state," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 205-237, March.
    7. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-628, May.
    8. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-Perfect ϵ-Equilibria in Perfect Information Games with Common Preferences at the Limit," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1208-1221, November.
    9. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
    10. Roger A. Purves & William D. Sudderth, 2011. "Perfect Information Games with Upper Semicontinuous Payoffs," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 468-473, August.
    11. Flesch, J. & Kuipers, J. & Schoenmakers, G. & Vrieze, K., 2013. "Subgame-perfection in free transition games," European Journal of Operational Research, Elsevier, vol. 228(1), pages 201-207.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. P. Jean-Jacques Herings & Harold Houba, 2022. "Costless delay in negotiations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 69-93, July.

    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. János Flesch & Arkadi Predtetchinski, 2017. "A Characterization of Subgame-Perfect Equilibrium Plays in Borel Games of Perfect Information," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1162-1179, November.
    2. János Flesch & Arkadi Predtetchinski, 2020. "Parameterized games of perfect information," Annals of Operations Research, Springer, vol. 287(2), pages 683-699, April.
    3. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-Perfect ϵ-Equilibria in Perfect Information Games with Common Preferences at the Limit," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1208-1221, November.
    4. Carlos Alós-Ferrer & Klaus Ritzberger, 2017. "Characterizing existence of equilibrium for large extensive form games: a necessity result," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 407-430, February.
    5. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2021. "Multi-lateral strategic bargaining without stationarity," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    6. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-perfect $$\epsilon $$ ϵ -equilibria in perfect information games with sigma-discrete discontinuities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 479-495, March.
    7. He, Wei & Sun, Yeneng, 2020. "Dynamic games with (almost) perfect information," Theoretical Economics, Econometric Society, vol. 15(2), May.
    8. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.
    9. J. Kuipers & J. Flesch & G. Schoenmakers & K. Vrieze, 2016. "Subgame-perfection in recursive perfect information games, where each player controls one state," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 205-237, March.
    10. Kuipers, J. & Flesch, J. & Schoenmakers, G. & Vrieze, K., 2009. "Pure subgame-perfect equilibria in free transition games," European Journal of Operational Research, Elsevier, vol. 199(2), pages 442-447, December.
    11. Flesch, Janos & Herings, P. Jean-Jacques & Maes, Jasmine & Predtetchinski, Arkadi, 2019. "Individual upper semicontinuity and subgame perfect ϵ-equilibria in games with almost perfect information," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
    12. Kuipers, J. & Flesch, J. & Schoenmakers, G.M. & Vrieze, K., 2008. "Pure subgame-perfect equilibria in free transition games," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    13. Duggan, John, 2017. "Existence of stationary bargaining equilibria," Games and Economic Behavior, Elsevier, vol. 102(C), pages 111-126.
    14. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.
    15. P. Jean-Jacques Herings & Harold Houba, 2022. "Costless delay in negotiations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 69-93, July.
    16. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.
    17. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2022. "Individual upper semicontinuity and subgame perfect $$\epsilon $$ ϵ -equilibria in games with almost perfect information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 695-719, April.
    18. János Flesch & Jeroen Kuipers & Ayala Mashiah-Yaakovi & Gijs Schoenmakers & Eran Shmaya & Eilon Solan & Koos Vrieze, 2014. "Non-existence of subgame-perfect $$\varepsilon $$ ε -equilibrium in perfect information games with infinite horizon," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 945-951, November.
    19. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2021. "Simple collective equilibria in stopping games," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    20. Steven J. Brams & Mehmet S. Ismail, 2022. "Every normal-form game has a Pareto-optimal nonmyopic equilibrium," Theory and Decision, Springer, vol. 92(2), pages 349-362, March.

    More about this item

    Keywords

    Perfect information game; Recursive game; Subgame perfect equilibrium;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:spr:joecth:v:71:y:2021:i:2:d:10.1007_s00199-020-01260-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.