IDEAS home Printed from https://ideas.repec.org/p/esj/esridp/084.html
   My bibliography  Save this paper

A Result for Approximation of Imitational Behavior in Large Populations

Author

Listed:
  • TANABE Yasuo

Abstract

This paper rigorously justifies the approximation of aggregate imitational behavior in large populations by the deterministic dynamics given by Bjonerstedt and Weibull. We first clarify what models fit their formulation, in which the stochastic dynamics depends only on the average frequencies of strategies in populations. Then we show that the stochastic process of each individual's behavior converges to a common McKean process and the average frequencies come to represent the deterministic dynamics of Bjonerstedt and Weibull when the number of individuals goes to infinity. Another derivation of replicator dynamics is also given by application to specific models of imitational behavior.

Suggested Citation

  • TANABE Yasuo, 2004. "A Result for Approximation of Imitational Behavior in Large Populations," ESRI Discussion paper series 084, Economic and Social Research Institute (ESRI).
    • Handle: RePEc:esj:esridp:084
    as

    Download full text from publisher

    File URL: http://www.esri.go.jp/jp/archive/e_dis/e_dis090/e_dis084a.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Borgers, Tilman & Sarin, Rajiv, 2000. "Naive Reinforcement Learning with Endogenous Aspirations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 921-950, November.
    2. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    3. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    4. Dixon, Huw David, 2000. "Keeping up with the Joneses: competition and the evolution of collusion," Journal of Economic Behavior & Organization, Elsevier, vol. 43(2), pages 223-238, October.
    5. Jonas Bjoernerstedt & Karl H. Schlag, "undated". "On the Evolution of Imitative Behavior," ELSE working papers 029, ESRC Centre on Economics Learning and Social Evolution.
    6. Cabrales, Antonio, 2000. "Stochastic Replicator Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-481, May.
    7. 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.
    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. repec:esj:esridp:84 is not listed on IDEAS
    2. Ponti, Giovanni, 2000. "Continuous-time evolutionary dynamics: theory and practice," Research in Economics, Elsevier, vol. 54(2), pages 187-214, June.
    3. Weibull, Jorgen W., 1998. "Evolution, rationality and equilibrium in games," European Economic Review, Elsevier, vol. 42(3-5), pages 641-649, May.
    4. Tanabe, Yasuo, 2006. "The propagation of chaos for interacting individuals in a large population," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 125-152, March.
    5. Uriarte, Jose Ramon, 2007. "A behavioural foundation for models of evolutionary drift," Journal of Economic Behavior & Organization, Elsevier, vol. 63(3), pages 497-513, July.
    6. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    7. Napel, Stefan, 2003. "Aspiration adaptation in the ultimatum minigame," Games and Economic Behavior, Elsevier, vol. 43(1), pages 86-106, April.
    8. Uriarte Ayo, José Ramón, 2005. "A Behavioral Foundation for Models of Evolutionary Drift," IKERLANAK 2005-19, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    9. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
    10. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April.
    11. Mohlin, Erik & Östling, Robert & Wang, Joseph Tao-yi, 2020. "Learning by similarity-weighted imitation in winner-takes-all games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 225-245.
    12. Knudsen, Thorbjørn, 2008. "Reference groups and variable risk strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 66(1), pages 22-36, April.
    13. Alanyali, Murat, 2010. "A note on adjusted replicator dynamics in iterated games," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 86-98, January.
    14. Dai, Darong, 2012. "On the Existence of Pareto Optimal Endogenous Matching," MPRA Paper 43125, University Library of Munich, Germany.
    15. Pierre Courtois & Tarik Tazdaït, 2012. "Learning to trust strangers: an evolutionary perspective," Journal of Evolutionary Economics, Springer, vol. 22(2), pages 367-383, April.
    16. Battalio,R. & Samuelson,L. & Huyck,J. van, 1998. "Risk dominance, payoff dominance and probabilistic choice learning," Working papers 2, Wisconsin Madison - Social Systems.
    17. repec:ehu:ikerla:6419 is not listed on IDEAS
    18. Nyborg, Karine & Rege, Mari, 2003. "On social norms: the evolution of considerate smoking behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 52(3), pages 323-340, November.
    19. Cabrales, Antonio & Uriarte Ayo, José Ramón, 2008. "Doubts and Equilibria," IKERLANAK 2008-31, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    20. Bosch-Domenech, Antoni & Saez-Marti, Maria, 2001. "Cycles of Aggregate Behavior in Theory and Experiment," Games and Economic Behavior, Elsevier, vol. 36(2), pages 105-137, August.
    21. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
    22. Jorge Andrés Gallego Durán & Rafal Raciborski, 2008. "Clientelism, income inequality, and social preferences: an evolutionary approach to poverty traps," Documentos de Economía 4717, Universidad Javeriana - Bogotá.

    More about this item

    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:esj:esridp:084. 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: HORI nobuko The email address of this maintainer does not seem to be valid anymore. Please ask HORI nobuko to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/esrgvjp.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.