Mechanism design with financially constrained agents and costly verification

A principal distributes an indivisible good to budget‐constrained agents when both valuation and budget are agents' private information. The principal can verify an agent's budget at a cost. The welfare‐maximizing mechanism can be implemented via a two‐stage scheme. First, agents report their budgets, receive cash transfers, and decide whether to enter a lottery over the good. Second, recipients of the good can sell it on a resale market but must pay a sales tax. Low‐budget agents receive a higher cash transfer, pay a lower price to enter the lottery, and face a higher sales tax. They are also randomly inspected.

Disequilibrium Trade in a Large Market for an Indivisible Good

Disequilibrium trade can occur in a market lacking both recontracting and a computational system that maps utilities into prices. This paper studies disequilibrium trade in a large market for an indivisible good. We focus on the possible speed of adjustment when arbitrage among periods is feasible and the surplus loss. We find that incentive compatible sequential trade through a disequilibrium path is only compatible with sluggish price adjustments and sufficiently impatient agents. Thus, price adjustment does not depend on excess demand alone but on arbitrage opportunities and the willingness of agents to engage on them. We find that the upper bound on the speed of price adjustment involves a lower bound for the social surplus loss, whatever the kind of rationing. The reason is that even when the market price converges to the surplus maximizing value, as it happens when rationing is efficient, some pieces of surplus are not attainable at the current period due to arbitrage. Moreover, faster price adjustments do not imply less surplus loss, because the effect of price changes on transactions via arbitrage. Finally, under weaker-than-efficient rationing there is a one period incentive compatible trading procedure in which most of the surplus is destroyed. The procedure has the property that almost every agent in the market trades.

Dynamic Signaling with Dropout Risk

We study the role of dropout risk in dynamic signaling. A seller privately knows the quality of an indivisible good and decides when to trade. In each period, he may draw a dropout shock that forces him to trade immediately. To avoid costly delay, the seller with a low-quality good voluntarily pools with early dropouts, implying that the expected quality of the good increases over time. We characterize the time-varying equilibrium trading dynamics. It is demonstrated that the maximum equilibrium delay of trade is decreasing in the initial belief that the good is of high quality. (JEL C73, D82, D83)

Fairness and the Strengths of Agents’ Claims

John Broome has proposed a theory of fairness according to which fairness requires that agents’ claims to goods be satisfied in proportion to the relative strength of those claims. In the case of competing claims for a single indivisible good, Broome argues that what fairness requires is the use of a weighted lottery as a surrogate to satisfying the competing claims: the relative chance of each claimant's winning the lottery should be set to the relative strength of each claimant's claim. In this journal, James Kirkpatrick and Nick Eastwood have objected that the use of weighted lotteries in the case of indivisible goods is unacceptable. In this article, I explain why Kirkpatrick and Eastwood's objection misses its mark.