Payoffs-Beliefs Duality and the Value of Information

Michel de Lara (1) , Olivier Gossner (2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 X - École polytechnique

In decision problems under incomplete information, 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 convex analysis. We then derive 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, and apply our results to the marginal value of information.

Mots clés: payoffs-beliefs duality AMS classification: 46N10; value of information; convex analysis; payoffs-beliefs duality 8; 91B06

Domaines: Optimisation et contrôle [math.OC]; Economies et finances

Michel de Lara, Olivier Gossner. Payoffs-Beliefs Duality and the Value of Information. 2019. ⟨hal-01941006v2⟩