Optimal search, learning and implementation

We derive conditions on the learning environment which encompasses both Bayesian and non-Bayesian processes ensuring that an e¢ cient allocation of resources is achievable in a dynamic allocation environment where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents’values. There are two main kind of conditions: 1) Higher observations should lead to more optimistic beliefs about the distribution of future values; 2) The allowed optimism associated with higher observations needs to be carefully bounded. Our analysis reveals and exploits close, formal relations between the problem of ensuring monotone and hence implementable allocation rules in our dynamic allocation problems with incomplete information and learning, and between the classical problem of …nding optimal stopping policies for search that are characterized by a reservation price property 1 Introduction In this paper we derive conditions on the learning process ensuring that an e¢ cient allocation of resources is implementable in a dynamic allocation environment, where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents’values. We wish to thank Sergiu Hart and Philippe Jehiel for several helpful remarks. We thank participants in seminars at the Paris School of Economics, Hebrew University , and Tel-Aviv University for their comments. We are grateful to the German Science Foundation for …nancial support. Gershkov, Moldovanu: Department of Economics, University of Bonn, [email protected]; [email protected]