A Logical Characterization of Iterated Admissibility

TL;DR

This paper provides a logical characterization of iterated admissibility using standard probability, applicable in all structures, and introduces a stronger notion called strong admissibility that captures agents' knowledge about rationality.

Contribution

It offers a logical framework for iterated admissibility that does not rely on complete structures and introduces strong admissibility to better model agents' knowledge.

Findings

Logical characterization of iterated admissibility with standard probability.

Applicable in all structures, not just complete ones.

Introduction of strong admissibility capturing agents' knowledge.

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 charaacterization of iterated admisibility is given that involves only standard probability and holds in all structures, not just complete structures. A stronger notion of strong admissibility is then defined. Roughly speaking, strong admissibility is meant to capture the intuition that "all the agent knows" is that the other agents satisfy the appropriate rationality assumptions. Strong admissibility makes it possible to relate admissibility, canonical structures (as typically considered in completeness proofs in modal logic), complete structures, and the notion of ``all I know''.