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An Adaptive Learning Model in Coordination Games
Department of Economics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
Received: 15 September 2013; in revised form: 4 November 2013 / Accepted: 7 November 2013 / Published: 15 November 2013
Abstract: 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.
Keywords: payoff assessment; learning; coordination games
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MDPI and ACS Style
Funai, N. An Adaptive Learning Model in Coordination Games. Games 2013, 4, 648-669.
Funai N. An Adaptive Learning Model in Coordination Games. Games. 2013; 4(4):648-669.
Funai, Naoki. 2013. "An Adaptive Learning Model in Coordination Games." Games 4, no. 4: 648-669.