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

In a Bayesian game some players might receive a noisy signal regarding the specific game actually being played before it starts. We study zero-sum games where each player receives a partial information about his own type and no information about that of the other player, and analyze the impact the signals have on the payoffs. It turns out that the functions that evaluate the value of information share two property. The first is Blackwell monotonicity, which means that each player gains from knowing more. The second is concavity on the space of conditional probabilities. ∗CES-équipe cermsem, Université Paris 1-Panthéon Sorbonne, 112 Boulevard de l’hôpital, 73013 Paris, France; e-mail:[email protected] †School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel; e-mail: [email protected]; home page: www.math.tau.ac.il/∼lehrer ‡LAGA Institut Galilée, Université Paris 13, avenue Jean Baptiste Clément, 93430 Villetaneuse, France; e-mail: [email protected] §This paper extends a paper by the last two authors that bears the same title. Journal of Economic Literature classification numbers: C72, C73, D80, D82, D83. Document de Travail du Centre d'Economie de la Sorbonne 2009.35 ha ls hs -0 03 90 62 5, v er si on 1 2 Ju n 20 09