Standard State Space Models of Unawareness (Extended Abstract)

TL;DR

This paper challenges a prior impossibility theorem, clarifies the modeling of awareness in state-space models, and demonstrates their simplicity and effectiveness for representing different notions of awareness.

Contribution

It refutes the claim that standard state-space models cannot represent unawareness and shows their applicability to multiple awareness notions with advantages in analysis.

Findings

Dekel, Lipman and Rustichini's theorem does not prove the impossibility.

Standard state-space models can represent two of three notions of awareness.

These models facilitate proofs of completeness, decidability, and integration of propositional quantifiers.

Abstract

The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, standard space models of these forms of awareness are attractively simple. They allow us to prove completeness and decidability results with ease, to carry over standard techniques from decision theory, and to add propositional quantifiers straightforwardly.