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Handbook of Game Theory by Shmuel Zamir, Petyon Young

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4.4.3 Changing types

Perhaps the most obvious route to a model in which reputation considerations persist is to assume that player 1's type is not fixed once-and-for-all at the beginning of the game, but is subject to persistent shocks. Intuitively, one's response upon having an uncharacteristically disappointing experience at a restaurant may be not “my previous experiences must have been atypical, and hence I should revise my posterior,” but rather “perhaps something has changed.” In this case, opponents will never be completely certain of a player's type. At first glance, it would seem that this can only reinforce the temporary-reputation arguments of Cripps et al. (2004, 2007), making it more difficult to find persistent reputation effects. ...

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