Filling Positions Without Transfers: Screening on Outside Options

TL;DR

This paper studies how a designer can optimally assign differentiated positions to agents with private outside options without transfers, using lotteries and screening to maximize acceptance.

Contribution

It characterizes the optimal mechanism for screening agents with private outside options, showing when uniform lotteries suffice and when menus are needed.

Findings

Optimal mechanism offers identical lotteries under certain conditions.

Mechanisms may require menus of lotteries when conditions are not met.

Participation probabilities can be decomposed to analyze feasibility.

Abstract

A designer offers vertically-differentiated positions to agents in the absence of transfers. Agents have private outside options and may reject their offers ex-post. The designer has preferences over the quantity of agents who accept each position. We show that under a general condition on the distribution of outside options, an optimal mechanism for the designer offers all agents an identical lottery, and we characterize this mechanism. When our condition does not hold, the optimal mechanism may require screening agents by offering a menu of distinct lotteries. Our results follow from a decomposition of agents' participation probabilities in any feasible mechanism.