Refinements of rationalizability for normal-form games

Refinements of rationalizability for normal-form games

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Article ID: iaor20001680
Country: Germany
Volume: 28
Issue: 1
Start Page Number: 53
End Page Number: 68
Publication Date: Jan 1999
Journal: International Journal of Game Theory
Authors: ,
Keywords: Nash theory and methods
Abstract:

There exist three equivalent definitions of perfect Nash equilbria which differ in the way ‘best responses against small perturbations’ are defined. It is shown that applying the spirit of these definitions to rationalizability leads to three different refinements of rationalizable strategies which are termed perfect, weakly perfect and trembling-hand perfect rationalizability, respectively. We prove that weakly perfect rationalizability is weaker than both perfect and proper rationalizability and in two-player games it is weaker than trembling-hand perfect rationalizability. By means of examples, it is shown that no other relationships can be found.

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