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Imitation, local interaction, and coordination

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  • Hsiao-Chi Chen

    ()

  • Yunshyong Chow

    ()

  • Li-Chau Wu

    ()

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    Abstract

    This paper analyzes players’ long-run behavior in evolutionary coordination games with imitation and one-dimensional local interaction. Players are assumed to interact with their two neighbors and to imitate actions with the highest average payoffs. We find that the payoff-dominant equilibrium survives in the long run with positive probability. The results derive the conditions under which both risk-dominant-strategy and payoff-dominant-strategy takers co-exist in the long run. The risk-dominant equilibrium is the unique long-run equilibrium for the remaining cases. This study extends and complements the analyses of Eshel et al. (Am Econ Rev 88:157–179, 1998 ) and Vega-Redondo (Evolution, games, and economic behaviour, 1996 ). Combining Alós-Ferrer and Weidenholzer’s (Econ Lett 93:163–168, 2006 ; J Econ Theory 14:251–274, 2008 ) and our results, we conclude that players’ long-run behavior varies with imitation rules and information collecting modes. Finally, we show the convergence rate to all the long-run equilibria. Copyright Springer-Verlag Berlin Heidelberg 2013

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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Game Theory.

    Volume (Year): 42 (2013)
    Issue (Month): 4 (November)
    Pages: 1041-1057

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    Handle: RePEc:spr:jogath:v:42:y:2013:i:4:p:1041-1057

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    Related research

    Keywords: Coordination game; Imitation; Local interaction; C72; C73; D83;

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    References

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    1. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
    2. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
    3. Jose Apesteguia & Steffen Huck & Jörg Oechssler, 2003. "Imitation - Theory and Experimental Evidence," Bonn Econ Discussion Papers bgse20_2003, University of Bonn, Germany, revised Aug 2004.
    4. Robles, Jack, 1998. "Evolution with Changing Mutation Rates," Journal of Economic Theory, Elsevier, vol. 79(2), pages 207-223, April.
    5. M. Kandori & R. Rob, 2010. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Levine's Working Paper Archive 502, David K. Levine.
    6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    7. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, Open Access Journal, vol. 1(4), pages 551-585, November.
    8. 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.
    9. A. Banerjee & Drew Fudenberg, 2010. "Word-of-Mouth Communication and Social Learning," Levine's Working Paper Archive 425, David K. Levine.
    10. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    11. BERGIN, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Alos-Ferrer, Carlos & Weidenholzer, Simon, 2006. "Imitation, local interactions, and efficiency," Economics Letters, Elsevier, vol. 93(2), pages 163-168, November.
    13. Jeffrey C. Ely, 2002. "Local Conventions," Discussion Papers 1349, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Ahmed Anwar, 2004. "On the Co-Existence of Conventions," ESE Discussion Papers 68, Edinburgh School of Economics, University of Edinburgh.
    15. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
    16. Ely Jeffrey C, 2002. "Local Conventions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 2(1), pages 1-32, May.
    17. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
    18. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
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    Cited by:
    1. Cui, Zhiwei, 2014. "More neighbors, more efficiency," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 103-115.

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