Dynamic Bayesian Persuasion with a Privately Informed Receiver

We study a dynamic Bayesian persuasion framework in a finite horizon setting consisting of a Seller and a Buyer. The Seller wishes to persuade the Buyer to buy a durable good at a given price by providing information about its relevance (match quality). The Buyer has private information about his valuation for a good match and we study optimal dynamic information policies employed by the Seller in equilibrium. For a fixed horizon, we show that the Seller always provides signals which truthfully convey a good match but may garble a bad one. Moreover, if the good is not bought in the first stage, the Seller provides information which improves over time. The agents always interact for a fixed amount of time within which a purchase decision is made. The length of this interaction remains fixed even for long horizons and depends only on the prior on the Buyer’s valuation. As the horizon goes to infinity, the bulk of the information about match quality is provided in the first period. This allows the Buyer to extract a large amount of information from the Seller at the beginning of their interaction. Even a slight probability of the Buyer being difficult to convince facilitates close to full disclosure immediately. ∗I wish to express my deepest gratitude towards my advisor Kalyan Chatterjee for his guidance, encouragement and support. I also wish to thank S. Nageeb Ali, Yeon-Koo Che, Brendan Daley, Henrique de Oliviera, Laura Doval, Edward Green, Benjamin Golub, Emir Kamenica, Navin Kartik, Willemien Kets, Vijay Krishna, Rohit Lamba, Laurent Mathevet, TymofiyMylovanov, Ron Siegel and Neil Wallace for useful comments, discussions and suggestions. All errors are my own. †Department of Economics, Penn State University ; Email : [email protected]