Rational inattention and the monotone likelihood ratio property

This paper explores the connection between rational inattention and the monotone likelihood ratio property (MLRP). In many economic problems, agents prefer to take a higher action when there is a higher underlying state. It is often assumed that these agents have noisy signals that are strongly correlated with the underlying state, i.e. ordered by the MLRP. Separately, a large literature has recently explored the behavior of rationally inattentive agents. Under some common separability and smoothness assumptions on the class of attention costs, I show that agents will always acquire signals that are ordered by the MLRP within such economic problems if and only if they have attention costs proportional to entropy reduction. With any other attention costs, agents err regarding the relative benefit of actions at different states. Extending to games, I provide conditions under which players first acquire MLRP-ordered signals, and then choose higher actions given higher signals. I then apply these results to independent private-value auctions.