Dynamic Mechanism Design: Dynamic Arrivals and Changing Values

Résumé

We study the optimal mechanism in a dynamic sales relationship where the buyer's arrival date is uncertain, and where his value changes stochastically over time. The buyer's arrival date is the first date at which contracting is feasible and is his private information. To induce immediate participation, the buyer is granted positive expected rents even if his value at arrival is the lowest possible. The buyer is punished for arriving late; i.e., he expects to earn less of the surplus. Optimal allocations for a late arriver are also further distorted below first-best levels. Conditions are provided under which allocations converge to the efficient ones long enough after contracting, and this convergence occurs irrespective of the time the contract is initially agreed (put differently, the so-called “principle of vanishing distortions” introduced by Battaglini (2005) continues to apply irrespective of the buyer's arrival date).