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An Adaptive Learning Model in Coordination Games

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  • Naoki Funai
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    Abstract

    In this paper, we provide a theoretical prediction of the way in which adaptive players behave in the long run in games with strict Nash equilibria. In the model, each player picks the action which has the highest assessment, which is a weighted average of past payoffs. Each player updates his assessment of the chosen action in an adaptive manner. Almost sure convergence to a Nash equilibrium is shown under one of the following conditions: (i) that, at any non-Nash equilbrium action profile, there exists a player who can find another action which gives always better payoffs than his current payoff, (ii) that all non-Nash equilibrium action profiles give the same payoff. We show almost sure convergence to a Nash equilibrium in the following games: pure coordination games; the battle of the sexes games; the stag hunt game; and the first order static game. In the game of chicken and market entry games, players may end up playing a maximum action profile.

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    File URL: ftp://ftp.bham.ac.uk/pub/RePEc/pdf/13-14.pdf
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    Bibliographic Info

    Paper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number 13-14.

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    Length: 43 pages
    Date of creation: Jun 2013
    Date of revision:
    Handle: RePEc:bir:birmec:13-14

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    Postal: Edgbaston, Birmingham, B15 2TT
    Web page: http://www.economics.bham.ac.uk
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    Related research

    Keywords: Adaptive Learning; Coordination Games;

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    1. Alan Beggs, 2002. "On the Convergence of Reinforcement Learning," Economics Series Working Papers 96, University of Oxford, Department of Economics.
    2. John B Van Huyck & Raymond C Battalio & Richard O Beil, 1997. "Tacit coordination games, strategic uncertainty, and coordination failure," Levine's Working Paper Archive 1225, David K. Levine.
    3. Cooper, Russell, et al, 1990. "Selection Criteria in Coordination Games: Some Experimental Results," American Economic Review, American Economic Association, vol. 80(1), pages 218-33, March.
    4. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
    5. Sarin, R. & Vahid, F., 1999. "Predicting how People Play Games: a Simple Dynamic Model of Choice," Monash Econometrics and Business Statistics Working Papers 12/99, Monash University, Department of Econometrics and Business Statistics.
    6. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
    7. Chen, Yan & Khoroshilov, Yuri, 2003. "Learning under limited information," Games and Economic Behavior, Elsevier, vol. 44(1), pages 1-25, July.
    8. Sarin, Rajiv & Vahid, Farshid, 1999. "Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 28(2), pages 294-309, August.
    9. Sarin, Rajiv, 1999. "Simple play in the Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 40(1), pages 105-113, September.
    10. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    11. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
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