Dynamic mechanism design: Dynamic arrivals and changing values

Abstract

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).

On the benefits of dynamic bidding when participation is costly

“…This paper shows that complete transparency is better for the seller than complete secrecy, but the optimal policy may be substantially more complex. 12 Part One: (2), (3) are sufficient for STE. Consider first bidder i's decision what to bid, assuming that he enters when specified by the entry thresholds (e 1 , .…”

“…9 The dynamic mechanism design literature has continued to grow quickly. A few recent notable contributions: Pavan, Segal, and Toikka [26] considers a general setting with changing agent preferences in which all are available to participate when the principal fixes the mechanism; Hinnosaar [14], Garrett [11] and Gershkov, Moldavanu, and Strack [13] consider settings with fixed preferences in which agents arrive over time according to a random process; and Ely, Garrett, and Hinnosaar [7] and Garrett [12] consider environments with both changing preferences and random arrivals.…”

Introduction to Symposium on Dynamic Contracts and Mechanism Design

“…In most of the contributions to this literature, the agents arrive stochastically over time but perfectly learn their values upon arrival, as for example in Said (2011Said ( , 2012. In contrast, Garrett (2014), Hinnosaar (2015), and Ely et al (2015) consider models in which agents gradually arrive and learn their values over time. A maintained assumption is that the time at which each agent learns his valuation is independent of the realized valuations.…”

“…By overbooking, the seller biases the allocation problem against the late-arriving buyers, thus incentivizing early purchases by early-arriving buyers. The paper by Garrett (2014) considers a related problem with time-varying valuations, similar to the one in Battaglini (2005) but where agents arrive stochastically over time and have private information about their arrival dates. It shows that the seller needs to provide early-arriving buyers with additional incentives to join immediately, and that all types, even the lowest, must receive a positive information rent.…”

“…Garrett (2013) characterizes the optimal contracts for the provision of a durable good in a setting in which agents arrive stochastically and their valuations change over time. Garrett (2014) in turn extends the analysis to contracts for the provision of non-durable services, as in Battaglini (2005). Similarly, Bergemann and Strack (2015b) offer an analysis of stationary contracts in the continuous-time environment of Bergemann and Strack (2015a); the requirement of stationarity is meant to restrict the principal to offering identical contracts to all future incoming generations.…”