Payoffs-beliefs duality and the value of information

De Lara, Michel and Gossner, Olivier ORCID: 0000-0003-3950-0208 (2020) Payoffs-beliefs duality and the value of information. SIAM Journal on Optimization, 30 (1). 464 - 489. ISSN 1052-6234

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Abstract

In decision problems under incomplete information, actions (identified to payoff vectors indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the value of information, using concepts and tools from convex analysis. We define the value function as the support function of the set of available actions: the subdifferential at a belief is the set of optimal actions at this belief; the set of beliefs at which an action is optimal is the normal cone of the set of available actions at this point. Our main results are (1) a necessary and sufficient condition for positive value of information and (2) global estimates of the value of information of any information structure from local properties of the value function and of the set of optimal actions taken at the prior belief only. We apply our results to the marginal value of information at the null, that is, when the agent is close to receiving no information at all, and we provide conditions under which the marginal value of information is infinite, null, or positive and finite.

Item Type:	Article
Official URL:	https://epubs.siam.org/journal/sjope8
Additional Information:	© 2020 Society for Industrial and Applied Mathematics
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics B Philosophy. Psychology. Religion > BC Logic
Date Deposited:	29 Nov 2019 08:33
Last Modified:	12 Dec 2024 01:59
URI:	http://eprints.lse.ac.uk/id/eprint/102682

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