Progressive Participation
Abstract
A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation.
We derive the optimal stationary mechanism, characterize its qualitative structure and derive a closed form solution. As the arrival time is private information, the agent can choose the time at which he reports his arrival. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem. The stopping time determines the time at which the agent decides to participate in the mechanism. The resulting value function of each agent can not be too convex and has to be continuously differentiable everywhere, re ecting the option value of delaying participation. The optimal mechanism thus induces progressive participation by each agent: he participates either immediately or at a future random time.
Bio
Dirk Bergemann is Douglass and Marion Campbell Professor of Economics at Yale University. He has secondary appointments as Professor of Computer Science at the School of Engineering and Professor of Finance at the School of Management. He was Chair of the Department of Economics from 2013-2019 and Co-Editor of Econometrica from 2014-2018. He has been affiliated with the Cowles Foundation for Research in Economics at Yale since 1996 and a fellow of the Econometric Society since 2007. His research is in the area of game theory, contract theory and venture capital and mechanism design. His most recent work is in the area of dynamic mechanism design and dynamic pricing, robust mechanism design, and information design.
His research has been supported by grants from the National Science Foundation, the Alfred P. Sloan Research Fellowship, Google Faculty Fellow and the German National Science Foundation.
