Refinements of rationalizability for normal-form games

There exist three equivalent definitions of perfect Nash equilibria which d iffer in the way "best responses against small perturbations" are defined. It is shown that applying the spirit of these definitions to rationalizabil ity leads to three different refinements of rationalizable strategies which are termed perfect (Bernheim, 1984), weakly perfect and trembling-hand per fect rationalizability, respectively. We prove that weakly perfect rational izability is weaker than both perfect and proper (Schuhmacher, 1995) ration alizability and in two-player games it is weaker than trembling-hand perfec t rationalizability. By means of examples, it is shown that no other relati onships can be found.