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Mutual Knowledge of Rationality in the Electronic Mail Game

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  • Koji Takamiya
  • Akira Tanaka
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    Abstract

    This paper reexamines the paradoxical aspect of the electronic mail game (Rubinstein, 1989). The electronic mail game is a coordination game with payoff uncertainty. At a Bayesian Nash equilibrium of the game, players cannot achieve the desired coordination of actions even when a high order of mutual knowledge of payoff functions obtains. We want to make explicit the role of knowledge about rationality of players, not only that of payoff functions. For this purpose, we use an extended version of the belief system model developed by Aumann and Brandenburger (1995). We propose a certain way of embedding the electronic mail game in an belief system. And we show that for rational players to coordinate their actions, for any embedding belief systems, it is necessary that the upper bound order of mutual knowledge of payoff functions exceeds the upper bound order of mutual knowledge of rationality. This result implies that under common knowledge of rationality, the coordination never occurs, which is similar to Rubinstein's result. We point out, however, that there exists a class embedding belief systems for which the above condition is also sufficient for the desired coordination.

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    File URL: http://www.iser.osaka-u.ac.jp/library/dp/2006/DP0650.pdf
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    Bibliographic Info

    Paper provided by Institute of Social and Economic Research, Osaka University in its series ISER Discussion Paper with number 0650.

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    Date of creation: Mar 2006
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    Handle: RePEc:dpr:wpaper:0650

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    1. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    2. Uwe Dulleck, 2002. "The e-mail game revisited - Modeling rough inductive reasoning," Vienna Economics Papers 0211, University of Vienna, Department of Economics.
    3. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
    4. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
    5. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
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