IDEAS home Printed from https://ideas.repec.org/p/ulp/sbbeta/2007-25.html

Best-reply matching and the centipede game

Author

Listed:
  • Gisèle Umbhauer

Abstract

In their paper on Best-Reply Matching (BRM), Droste, Kosfeld & Voorneveld (2003) obtained quite intuitive results for the centipede game. In this short paper we first show that these results derive from the application of their criterion to the reduced normal form of the game. Then we prove that applying their criterion to the normal form of the game leads to different results. Third we propose an extension of Droste, Kosfeld & Voorneveld’s criterion, which leads to the same results in both the reduced normal form and the normal form of a game. This extension leads to a larger set of behaviors, including the Subgame Perfect Nash equilibrium but also a limited rationality behavior that strongly sustains the continuation of the game.

Suggested Citation

  • Gisèle Umbhauer, 2007. "Best-reply matching and the centipede game," Working Papers of BETA 2007-25, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    • Handle: RePEc:ulp:sbbeta:2007-25
    as

    Download full text from publisher

    File URL: http://beta.u-strasbg.fr/WP/2007/2007-25.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kosfeld, Michael & Droste, Edward & Voorneveld, Mark, 2002. "A myopic adjustment process leading to best-reply matching," Games and Economic Behavior, Elsevier, vol. 40(2), pages 270-298, August.
    2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    3. Droste, Edward & Kosfeld, Michael & Voorneveld, Mark, 2003. "Best-reply matching in games," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 291-309, December.
    4. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    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. Gisèle Umbhauer, 2017. "Second price all-pay auctions, how much money do players get or lose?," Working Papers of BETA 2017-16, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    2. Droste, Edward & Kosfeld, Michael & Voorneveld, Mark, 2003. "Best-reply matching in games," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 291-309, December.
    3. Gisèle Umbhauer, 2019. "Second-Price All-Pay Auctions and Best-Reply Matching Equilibria," Post-Print hal-03164468, HAL.
    4. Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 2000. "The equivalence of the Dekel-Fudenberg iterative procedure and weakly perfect rationalizability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 677-687.
    5. Ambrus, Attila, 2006. "Coalitional Rationalizability," Scholarly Articles 3200266, Harvard University Department of Economics.
    6. Dominiak, Adam & Lee, Dongwoo, 2023. "Testing rational hypotheses in signaling games," European Economic Review, Elsevier, vol. 160(C).
    7. Pei, Ting & Takahashi, Satoru, 2019. "Rationalizable strategies in random games," Games and Economic Behavior, Elsevier, vol. 118(C), pages 110-125.
    8. Lawrence Christiano & Husnu Dalgic & Xiaoming Li, 2022. "Modelling the Great Recession as a Bank Panic: Challenges," Economica, London School of Economics and Political Science, vol. 89(S1), pages 200-238, June.
    9. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    10. Jara-Moroni, Pedro, 2018. "Rationalizability and mixed strategies in large games," Economics Letters, Elsevier, vol. 162(C), pages 153-156.
    11. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    12. Alós-Ferrer, Carlos & Kuzmics, Christoph, 2013. "Hidden symmetries and focal points," Journal of Economic Theory, Elsevier, vol. 148(1), pages 226-258.
    13. Asheim, Geir B. & Dufwenberg, Martin, 2003. "Admissibility and common belief," Games and Economic Behavior, Elsevier, vol. 42(2), pages 208-234, February.
    14. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    15. Seel, Christian & Tsakas, Elias, 2017. "Rationalizability and Nash equilibria in guessing games," Games and Economic Behavior, Elsevier, vol. 106(C), pages 75-88.
    16. Isogai, Shigeki & Shen, Chaohai, 2023. "Multiproduct firm’s reputation and leniency program in multimarket collusion," Economic Modelling, Elsevier, vol. 125(C).
    17. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2023. "Social Rationalizability with Mediation," Dynamic Games and Applications, Springer, vol. 13(2), pages 440-461, June.
    18. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2019. "Comprehensive rationalizability," Games and Economic Behavior, Elsevier, vol. 116(C), pages 185-202.
    19. Arthur Charpentier & Romuald Élie & Carl Remlinger, 2023. "Reinforcement Learning in Economics and Finance," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 425-462, June.
    20. Christoph Kuzmics & Daniel Rodenburger, 2020. "A case of evolutionarily stable attainable equilibrium in the laboratory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 685-721, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:ulp:sbbeta:2007-25. 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: the person in charge The email address of this maintainer does not seem to be valid anymore. Please ask the person in charge to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/bestrfr.html .

    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.