Long information design and splitting games

Abstract

This work deals with strategic transmission of information between Bayesian players. In a first part I will present/recall the concepts of splitting and concavification operator, and we will see how the operator extends to dynamic contexts with constraints.Then 2-player zero-sum splitting games will be introduced. In a second part we will consider 2-player zero-sum dynamic splitting games, where the concavification operator will be further extended to general "Mertens-Zamir" operators. In particular we will introduce the notion of Mertens-Zamir transform of a real-valued matrix. More precisely, we study games between two players who want to influence the final action of a decision-maker. Each player controls the public information on a private persistent state, and in each period the players can disclose information to the decision-maker about their own state. Extending tools from repeated games with incomplete information, we study the value and optimal strategies depending on the timing of the game, the possible deadline and the possible restrictions on information revelation. Our analysis covers continuous unconstraint environments, the case where a subset of Blackwell experiments is available to the designers, as well as environments in which designers can only induce finite sets of posterior beliefs. There may be no bound on the number of communication stages required at equilibrium. (joint with F. Koessler, M. Laclau and T. Tomala)