A Rothschild-Stiglitz Approach to Bayesian Persuasion

* Gentzkow: Department of Economics, Stanford University, 579 Serra Mall, Office 321, Stanford, CA 94305 (e-mail: [email protected]); Kamenica: The University of Chicago Booth School of Business, 5807 S. Woodlawn Avenue, Chicago, IL 60637 (e-mail: [email protected]). We thank the Sloan Foundation and the University of Chicago Booth School of Business for financial support. † Go to http://dx.doi.org/10.1257/aer.p20161049 to visit the article page for additional materials and author disclosure statement(s). Consider a situation where one person, call him Sender, generates information in order to persuade another person, call her Receiver, to change her action. Sender and Receiver share a common prior about the state of the world. Sender can publicly generate any signal about the state and Receiver observes the signal realization before she takes her action. Kamenica and Gentzkow (2011) analyze a general version of this “Bayesian persuasion” problem. They draw on an insight from Aumann and Maschler (1995) to develop a geometric approach to Sender’s optimization problem. They derive a value function over beliefs and then construct the optimal signal from the concavification of that value function. This approach provides ample intuition about the structure of the optimal signal, but has limited applicability when the state space is large. The dimensionality of the space of beliefs is roughly the same as the cardinality of the state space, so the value function and its concavification can be visualized easily only when there are two or three states of the world. When the state space