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A Syntactic Approach to Rationality in Games

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  • Giacomo Bonanno

    (Department of Economics, University of California Davis)

Abstract

We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom says that a player is irrational if she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994).

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Bibliographic Info

Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 71.

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Length: 22
Date of creation: 27 Jan 2007
Date of revision:
Handle: RePEc:cda:wpaper:07-1

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Keywords: rationality; common belief; rationalizability; dominated strategies; game logic; frame characterization;

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  1. Werlang, Sérgio Ribeiro da Costa & Chin-Chiu Tan, Tommy, 1987. "The Bayesian Foundations of Solution Concepts of Games," Economics Working Papers (Ensaios Economicos da EPGE) 111, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
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