Bayesian Persuasion with Quadratic Preferences
51 Pages Posted: 19 Jan 2012 Last revised: 24 Mar 2018
Date Written: March 21, 2018
This paper examines the optimal information design within a Bayesian persuasion setup with multidimensional information. Assuming a linear-quadratic specification, I provide a new approach to the optimal information design by addressing the statistical properties of the receiver's posterior expectation about the state. I derive an upper bound of the gain from information design by formulating a semidefinite programming problem, and then show that the optimal policy can be the disclosure of multiple statistics constructed by linear combinations of the state when it has a multivariate normal distribution. Applications of the theory include price leadership strategy and central bank communication.
Keywords: Bayesian persuasion, multidimensional information design, information disclosure, quadratic preferences, semidefinite programming
JEL Classification: D82, D83
Suggested Citation: Suggested Citation