Long information design

Résumé

We analyze information design games between two designers with opposite preferences and a single agent. Before the agent makes a decision, designers repeatedly disclose public information about persistent state parameters. Disclosure continues until no designer wishes to reveal further information. We consider environments with general constraints on feasible information disclosure poli- cies. Our main results characterize equilibrium payoffs and strategies of this long information design game and compare them with the equilibrium outcomes of games where designers move only at a single predetermined period. When information disclosure policies are unconstrained, we show that at equilibrium in the long game, information is revealed right away in a single period; otherwise, the number of periods in which information is disclosed might be unbounded. As an application, we study a competition in product demonstration and show that more information is revealed if each designer could disclose information at a pre-determined period. The format that provides the buyer with most information is the sequential game where the last mover is the ex-ante favorite seller.

Mots-clés

Bayesian persuasion; concavification; convexification; information; design; Mertens–Zamir solution; product demonstration, splitting games; statis-; tical experiments; stochastic games.;