Rational inattention, optimal consideration sets, and stochastic choice

We unite two basic approaches to modelling limited attention in choice by showing that the rational inattention model implies the formation of consideration sets—only a subset of the available alternatives will be considered for choice. We provide necessary and sufficient conditions for rationally inattentive behaviour which allow the identification of consideration sets. In simple settings, chosen options are those that are best on a stand-alone basis. In richer settings, the consideration set can only be identified holistically. In addition to payoffs, prior beliefs impact consideration sets. Linear inequalities identify all priors consistent with each possible consideration set.