COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1672R

The Dynamic Pivot Mechanism

Dirk Bergemann and Juuso Välimäki

August 2008
Revised December 2009

We consider truthful implementation of the socially efficient allocation in an independent private-value environment in which agents receive private information over time. We propose a suitable generalization of the pivot mechanism, based on the marginal contribution of each agent. In the dynamic pivot mechanism, the ex-post incentive and ex-post participation constraints are satisfied for all agents after all histories. In an environment with diverse preferences it is the unique mechanism satisfying ex-post incentive, ex-post participation and efficient exit conditions.

We develop the dynamic pivot mechanism in detail for a repeated auction of a single object in which each bidder learns over time her true valuation of the object. The dynamic pivot mechanism here is equivalent to a modified second price auction.

Keywords: Pivot mechanisms, Dynamic mechanism design, Ex-post equilibrium, Marginal contribution, Multi-armed bandit, Bayesian learning

JEL Classifications: C72, C73, D43, D83