Information Design in Concave Games

Résumé

We study information design in games with a continuum of actions such that the players’ payoffs are concave in their own actions. A designer chooses an information structure–a joint distribution of a state and a private signal of each player. The information structure induces a Bayesian game and is evaluated according to the expected designer’s payoff under the equilibrium play. We develop a method that facilitates the search for an optimal information structure, i.e., one that cannot be outperformed by any other information structure, however complex. We show an information structure is optimal whenever it induces the strategies that can be implemented by an incentive contract in a dual, principal-agent problem which aggregates marginal payoffs of the players in the original game. We use this result to establish the optimality of Gaussian information structures in settings with quadratic payoffs and a multivariate normally distributed state. We analyze the details of optimal structures in a differentiated Bertrand competition and in a prediction game.

Mots-clés

Information design; Bayesian persuasion; Concave games; Duality; First-order approach;

Codes JEL

D42: Monopoly
D82: Asymmetric and Private Information • Mechanism Design
D83: Search • Learning • Information and Knowledge • Communication • Belief

Remplacé par

Takuro Yamashita et Alex Smolin, Information Design in Concave Games, EC'22: Proceedings of the 23rd ACM Conference on Economics and Computation, juillet 2022.