Dynamic mechanism design: Dynamic arrivals and changing values

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 …rst 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 …rst-best levels. Conditions are provided under which allocations converge to the e¢ cient ones long enough after contracting, and this convergence occurs irrespective of the time the contract is initially agreed (put di¤erently, the so-called "principle of vanishing distortions" introduced by Battaglini (2005) continues to apply irrespective of the buyer’s arrival date). JEL Classi…cation: D82 Keywords: dynamic mechanism design, dynamic arrivals, stochastic process This paper adapts the second part of my earlier work “Durable Goods Sales with Dynamic Arrivals and Changing Values” to a simpler setting where the good is not durable. The paper has bene…ted from detailed comments from Simon Board, Rahul Deb, Je¤ Ely, Igal Hendel, Konrad Mierendor¤, Alessandro Pavan, Bill Rogerson, Bruno Strulovici and Rakesh Vohra. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714147).