Long information design - Frédéric Koessler; Marie Laclau; Jérôme Renault; Tristan Tomala (Theoretical Economics, 2022)
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 policies. 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 predetermined period. The format that provides the buyer with most information is the sequential game where the last mover is the ex-ante favorite seller.
Keywords: C72; D82; 330; Bayesian persuasion; concavification; convexification; information design; Mertens-Zamir solution; product demonstration; splitting games; statistical experiments; stochastic games