Alex Bloedel
Date & Time
Jan 15, 2021
from
12:10 PM to
01:30 PM
Location
Zoom Social Science and Humanities
Description
https://ucdavis.zoom.us/j/95126379427?pwd=Q1JaN1RrL3lBWGxpREd3WmxFQXdndz09
Title: “The Cost of Optimally Acquired Information (with Weijie Zhong)”
Abstract: “This paper develops a theory for the expected cost of optimally acquired information when information can be acquired sequentially and there is no explicit cost of delay. We study the "reduced-form" Indirect Cost functions for information generated by sequential minimization of a "primitive" Direct Cost function. The class of Indirect Costs is characterized by a recursive condition called Sequential Learning-Proofness. This condition is inconsistent with Prior Invariance: Indirect Costs must depend on the decision-maker's prior beliefs.
We show that Sequential Learning-Proofness provides partial optimality foundations for the Uniformly Posterior Separable (UPS) cost functions used in the rational inattention literature: a cost function is UPS if and only if it is an Indirect Cost that (i) satisfies a mild regularity condition or, equivalently, (ii) is generated (only) by Direct Costs for which the optimal sequential strategy involves observing only Gaussian diffusion signals, a property we call Preference for Incremental Learning. We characterize the unique UPS cost function that is generated by a Prior Invariant Direct Cost; it exists only when there are exactly two states.
We also propose two specific UPS cost functions based on additional optimality principles. We introduce and characterize Total Information as the unique Indirect Cost that is Process Invariant when information can be decomposed both sequentially and "simultaneously": it is uniquely invariant to the "merging" and "splitting" of experiments. Under regularity conditions, Mutual Information is the unique Indirect Cost that is Compression Invariant when aspects of the state space can be "freely ignored": it is uniquely invariant to the to the "merging" and "splitting" of states. We discuss implications for applications of, and modeling debates within, the rational inattention literature.”
