Cautious Belief and Iterated Admissibility

TL;DR

This paper introduces cautious belief and cautious rationality concepts to characterize iterated admissibility in finite games, linking epistemic conditions with strategic solution concepts.

Contribution

It formalizes cautious belief notions and connects them to iterated admissibility, extending the epistemic characterization to arbitrary type structures and transparency scenarios.

Findings

Iterated admissibility corresponds to cautious rationality and common cautious belief in cautious rationality.

In arbitrary type structures, the self-admissible set characterizes the behavioral implications of these epistemic assumptions.

Similar results hold when cautiousness is transparent to players.

Abstract

We define notions of cautiousness and cautious belief to provide epistemic conditions for iterated admissibility in finite games. We show that iterated admissibility characterizes the behavioral implications of "cautious rationality and common cautious belief in cautious rationality" in a terminal lexicographic type structure. For arbitrary type structures, the behavioral implications of these epistemic assumptions are characterized by the solution concept of self-admissible set (Brandenburger, Friedenberg and Keisler 2008). We also show that analogous conclusions hold under alternative epistemic assumptions, in particular if cautiousness is "transparent" to the players. KEYWORDS: Epistemic game theory, iterated admissibility, weak dominance, lexicographic probability systems. JEL: C72.