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Perea, Andrés
Games and economic behavior, 06/2011, Letnik: 72, Številka: 2Journal Article
Proper rationalizability ( Schuhmacher, 1999; Asheim, 2001) is a concept in epistemic game theory based on the following two conditions: (a) a player should be cautious, that is, should not exclude any opponentʼs strategy from consideration; and (b) a player should respect the opponentsʼ preferences, that is, should deem an opponentʼs strategy s i infinitely more likely than s i ′ if he believes the opponent to prefer s i to s i ′ . A strategy is properly rationalizable if it can optimally be chosen under common belief in the events (a) and (b). In this paper we present an algorithm that for every finite game computes the set of all properly rationalizable strategies. The algorithm is based on the new idea of a preference restriction, which is a pair ( s i , A i ) consisting of a strategy s i , and a subset of strategies A i , for player i. The interpretation is that player i prefers some strategy in A i to s i . The algorithm proceeds by successively adding preference restrictions to the game.
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