Iterated Admissibility as Solution Concept in Game Theory

Admissibility, i.e. the deletion of weakly dominated strategies, is a highly controversia1 solution concept for non cooperative games. This paper proposes a complete theory of weak dominance and, contrary to almost al1 the literature on this topic, it provides positive results on foundations of iterated admissibility. The main contribution of this work is to show that (iterated) admissibility can be justified once payoffs' ties are seriously taken into considerations and players optimise taking into consideration the information provided by these ties, i.e. using strategic independent sets (Mailath at al. 1993) and conditional dominance (Shimoji and Watson 1998). In particular we prove that (iterated) maximal simultaneous deletion of weakly dominated strategies endogenously emerges as axiomatic characterization of iterated admissibility. As a consequence of this result, the paper provides axiomatic and Bayesian foundations of iterated admissibility, proves the logical consistency of (iterated) admissibility as solution concept in game theory, and that common knowledge of admissibility leads to iterated admissibility, showing why previous attempts using cautious behaviour were ineffective.