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

B. de Meyer, E. Lehrer, D. ROSENBERG

Mathematics of Operations Research

November 2010, vol. 35, n°4, pp.851-863

Departments: Economics & Decision Sciences, GREGHEC (CNRS)

Keywords: Value-of-information function, Zero-sum game, Game with incomplete information, Blackwell monotonicity

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