Payoffs-Beliefs Duality and the Value of Information - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Optimization Année : 2020

Payoffs-Beliefs Duality and the Value of Information

Résumé

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 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.
Fichier principal
Vignette du fichier
VoI_DeLara_Gossner_HAL3.pdf (928.59 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01941006 , version 1 (30-11-2018)
hal-01941006 , version 2 (05-08-2019)
hal-01941006 , version 3 (18-11-2019)

Identifiants

Citer

Michel de Lara, Olivier Gossner. Payoffs-Beliefs Duality and the Value of Information. SIAM Journal on Optimization, 2020, 30 (1), pp.464-489. ⟨10.1137/18M1230049⟩. ⟨hal-01941006v3⟩
146 Consultations
192 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More