Refinements of rationalizability for normal-form games

Herings, PJJ;Vannetelbosch, Vincent
(1999) International Journal of Game Theory — Vol. 28, n° 1, p. 53-68 (1999)

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Abstract
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.
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Herings, P., & Vannetelbosch, V. (1999). Refinements of rationalizability for normal-form games. International Journal of Game Theory, 28(1), 53-68. https://doi.org/10.1007/s001820050098 (Original work published 1999)