Evaluating Information in Zero-Sum Games with Incomplete Information on Both Sides

Dinah Rosenberg (1) , Bernard de Meyer (2) , Ehud Lehrer (3)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 CES - Centre d'économie de la Sorbonne
3 TAU - School of Mathematical Sciences [Tel Aviv]

We study zero-sum games with incomplete information and analyze the impact that the information players receive has on the payoffs. It turns out that the functions that measure the value of information share two properties. The first is Blackwell monotonicity, which means that each player gains from knowing more. The second is concavity on the space of conditional probabilities. We prove that any function satisfying these two properties is the value function of a zero-sum game.

Keywords: value-of-information function; zero-sum game; game with incomplete information; Blackwell monotonicity

Domains: Humanities and Social Sciences; Economics and Finance; Economy and decision science

Dinah Rosenberg, Bernard de Meyer, Ehud Lehrer. Evaluating Information in Zero-Sum Games with Incomplete Information on Both Sides. Mathematics of Operations Research, 2010, 35 (4), pp.851-863. ⟨10.1287/moor.1100.0467⟩. ⟨hal-00586037⟩