Refinements of rationalizability for normal-form games

There exist three equivalent definitions of perfect Nash equilibria 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 (Bernheim, 1984), weakly perfect and trembling-hand perfect rationalizability, respectively. We prove that weakly perfect rationalizability is weaker than both perfect and proper (Schuhmacher, 1995) 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.

Authors and Affiliations

1. CentER and Department of Econometrics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands (e-mail: P.J.J.Herings@kub.nl), , , , , , NL

   P. Jean-Jacques Herings

2. CORE, University of Louvain, voie du Roman Pays 34, B-1348 Louvain-la-Neuve, Belgium, , , , , , BE

   Vincent J. Vannetelbosch

Received: January 1997/final version: August 1998

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