A logical characterization of iterated admissibility

Abstract

Brandenburger, Friedenberg, and Keisler provide an epistemic characterization of iterated admissibility (i.e., iterated deletion of weakly dominated strategies) where uncertainty is represented using LPSs (lexicographic probability sequences). Their characterization holds in a rich structure called a complete structure, where all types are possible. Here, a logical characterization of iterated admissibility is given that involves only standard probability and holds in all structures, not just complete structures. Roughly speaking, our characterization shows that iterated admissibility captures the intuition that "all the agent knows" is that agents satisfy the appropriate rationality assumptions.

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