IDEAS home Printed from https://ideas.repec.org/p/huj/dispap/dp633.html
   My bibliography  Save this paper

The instability of backward induction in evolutionary dynamics

Author

Listed:
  • Zibo Xu

Abstract

This paper continues the work initiated in [19]. We adopt the same model as in [19]. We show that the non-backward-induction equilibrium component may be evolutionarily stable for any population size in a finite stopping game where the two equilibrium components are terminated by different players. A surprising result is that the backward induction equilibrium component may not be evolutionarily stable for large populations. Finally, we study the evolutionary stability result in a different limiting process where the expected number of mutations per generation is bounded away from both zero and infinity.

Suggested Citation

  • Zibo Xu, 2013. "The instability of backward induction in evolutionary dynamics," Discussion Paper Series dp633, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp633
    as

    Download full text from publisher

    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp633.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. J. Barkley Rosser Jr. (ed.), 2009. "Handbook of Research on Complexity," Books, Edward Elgar Publishing, number 3625.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. Binmore, Ken, 1996. "A Note on Backward Induction," Games and Economic Behavior, Elsevier, vol. 17(1), pages 135-137, November.
    5. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
    6. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    7. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    8. Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(1), pages 23-46.
    9. Cressman, R. & Schlag, K. H., 1998. "The Dynamic (In)Stability of Backwards Induction," Journal of Economic Theory, Elsevier, vol. 83(2), pages 260-285, December.
    10. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
    11. Ziv Gorodeisky, 2006. "Evolutionary Stability for Large Populations and Backward Induction," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 369-380, May.
    12. Kuzmics, Christoph, 2004. "Stochastic evolutionary stability in extensive form games of perfect information," Games and Economic Behavior, Elsevier, vol. 48(2), pages 321-336, August.
    13. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    14. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    15. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    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. Zibo Xu, 2013. "Evolutionary stability in general extensive-form games of perfect information," Discussion Paper Series dp631, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Xu, Zibo, 2013. "Stochastic stability in finite extensive-form games of perfect information," SSE/EFI Working Paper Series in Economics and Finance 743, Stockholm School of Economics.
    3. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    4. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
    5. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    6. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
    7. 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.
    8. Battalio,R. & Samuelson,L. & Huyck,J. van, 1998. "Risk dominance, payoff dominance and probabilistic choice learning," Working papers 2, Wisconsin Madison - Social Systems.
    9. Veller, Carl & Hayward, Laura K., 2016. "Finite-population evolution with rare mutations in asymmetric games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 93-113.
    10. Thierry Vignolo, 2010. "Imitation and selective matching in reputational games," Journal of Evolutionary Economics, Springer, vol. 20(3), pages 395-412, June.
    11. Jindani, Sam, 2022. "Learning efficient equilibria in repeated games," Journal of Economic Theory, Elsevier, vol. 205(C).
    12. Tassos Patokos, 2014. "Introducing Disappointment Dynamics and Comparing Behaviors in Evolutionary Games: Some Simulation Results," Games, MDPI, vol. 5(1), pages 1-25, January.
    13. Heller, Yuval & Kuzmics, Christoph, 2024. "Communication, renegotiation and coordination with private values," Games and Economic Behavior, Elsevier, vol. 143(C), pages 51-76.
    14. Neary, Philip R., 2012. "Competing conventions," Games and Economic Behavior, Elsevier, vol. 76(1), pages 301-328.
    15. Xu, Zibo, 2016. "Convergence of best-response dynamics in extensive-form games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 21-54.
    16. Rapoport, Amnon & Stein, William E. & Parco, James E. & Nicholas, Thomas E., 2003. "Equilibrium play and adaptive learning in a three-person centipede game," Games and Economic Behavior, Elsevier, vol. 43(2), pages 239-265, May.
    17. Jean Paul Rabanal & Daniel Friedman, 2015. "How Moral Codes Evolve in a Trust Game," Games, MDPI, vol. 6(2), pages 1-11, June.
    18. Lindgren, Kristian & Verendel, Vilhelm, 2013. "Evolutionary Exploration of the Finitely Repeated Prisoners' Dilemma--The Effect of Out-of-Equilibrium Play," MPRA Paper 43662, University Library of Munich, Germany.
    19. Kristian Lindgren & Vilhelm Verendel, 2013. "Evolutionary Exploration of the Finitely Repeated Prisoners’ Dilemma—The Effect of Out-of-Equilibrium Play," Games, MDPI, vol. 4(1), pages 1-20, January.
    20. Heller, Yuval & Kuzmics, Christoph, 2020. "Communication, Renegotiation and Coordination with Private Values (Extended Version)," MPRA Paper 102926, University Library of Munich, Germany, revised 26 Jul 2021.

    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:huj:dispap:dp633. 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: Michael Simkin (email available below). General contact details of provider: https://edirc.repec.org/data/crihuil.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.