The Cost of Optimally Acquired Information
Abstract/Contents
- 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 op timal sequential strategy involves observing only Gaussian diffusion signals. 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 as pects of the state space can be “freely ignored”: it is uniquely invariant to the “merging” and “splitting” of states. We argue that Total Information and Mutual Information represent the normatively ideal costs of, respectively, “producing” and “processing” information.
Description
| Type of resource | text |
|---|---|
| Date created | August 19, 2021 |
Creators/Contributors
| Author | Bloedel, Alexander W. |
|---|---|
| Author | Zhong, Weijie |
| Organizer of meeting | Board, Simon |
| Organizer of meeting | Cisternas, Gonzalo |
| Organizer of meeting | Frick, Mira |
| Organizer of meeting | Georgiadis, George |
| Organizer of meeting | Skrzypacz, Andrzej |
| Organizer of meeting | Sugaya, Takuo |
Subjects
| Subject | information acquisition |
|---|---|
| Subject | cost of information |
| Subject | dynamic information acquisition |
| Subject | sequential sampling |
| Subject | rational inattention |
| Genre | Text |
| Genre | Working paper |
| Genre | Grey literature |
Bibliographic information
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- User agrees that, where applicable, content will not be used to identify or to otherwise infringe the privacy or confidentiality rights of individuals. Content distributed via the Stanford Digital Repository may be subject to additional license and use restrictions applied by the depositor.
- License
- This work is licensed under a Creative Commons Attribution 4.0 International license (CC BY).
Preferred citation
- Preferred citation
- Bloedel, A. and Zhong, W. (2022). The Cost of Optimally Acquired Information. Stanford Digital Repository. Available at https://purl.stanford.edu/cj843yf9381
Collection
SITE Conference 2021
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