Pjj. Herings et Vj. Vannetelbosch, The equivalence of the Dekel-Fudenberg iterative procedure and weakly perfect rationalizability, ECON THEORY, 15(3), 2000, pp. 677-687
Two approaches have been proposed in the literature to refine the rationali
zability solution concept: either assuming that a player believes that with
small probability her opponents choose strategies that are irrational, or
assuming that their is a small amount of payoff uncertainty. We show that b
oth approaches lead to the same refinement if strategy perturbations are ma
de according to the concept of weakly perfect rationalizability, and if the
re is payoff uncertainty as in Dekel and Fudenberg [J, of Econ. Theory 52 (
1990), 243-267], For both cases, the strategies that survive are obtained b
y starting with one round of elimination of weakly dominated strategies fol
lowed by many rounds of elimination of strictly dominated strategies.