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An Adaptive Learning Model in Coordination Games

  • Naoki Funai

    ()

    (Department of Economics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK)

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    In this paper, we provide a theoretical prediction of the way in which adaptive players behave in the long run in normal form games with strict Nash equilibria. In the model, each player assigns subjective payoff assessments to his own actions, where the assessment of each action is a weighted average of its past payoffs, and chooses the action which has the highest assessment. After receiving a payoff, each player updates the assessment of his chosen action in an adaptive manner. We show almost sure convergence to a Nash equilibrium under one of the following conditions: (i) that, at any non-Nash equilibrium action profile, there exists a player who receives a payoff, which is less than his maximin payoff; (ii) that all non-Nash equilibrium action profiles give the same payoff. In particular, the convergence is shown in the following games: the battle of the sexes game, the stag hunt game and the first order statistic game. In the game of chicken and market entry games, players may end up playing the action profile, which consists of each player’s unique maximin action.

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    Article provided by MDPI, Open Access Journal in its journal Games.

    Volume (Year): 4 (2013)
    Issue (Month): 4 (November)
    Pages: 648-669

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    Handle: RePEc:gam:jgames:v:4:y:2013:i:4:p:648-669:d:30467
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    1. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-48, March.
    2. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
    3. 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.
    4. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, June.
    5. Laslier, Jean-Francois & Topol, Richard & Walliser, Bernard, 2001. "A Behavioral Learning Process in Games," Games and Economic Behavior, Elsevier, vol. 37(2), pages 340-366, November.
    6. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    7. Sarin, Rajiv, 1999. "Simple play in the Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 40(1), pages 105-113, September.
    8. Sarin, Rajiv & Vahid, Farshid, 2001. "Predicting How People Play Games: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 34(1), pages 104-122, January.
    9. 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.
    10. Chen, Yan & Khoroshilov, Yuri, 2003. "Learning under limited information," Games and Economic Behavior, Elsevier, vol. 44(1), pages 1-25, July.
    11. 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.
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