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Filling Positions Without Transfers: Screening on Outside Options

Morteza Honarvar, Joanna Krysta, Eric Tang

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.

Filling Positions Without Transfers: Screening on Outside Options

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.
Paper Structure (33 sections, 14 theorems, 61 equations, 8 figures)

This paper contains 33 sections, 14 theorems, 61 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Model
  4. Framework
  5. Direct Mechanisms
  6. Common Lotteries
  7. Discussion of Model
  8. Mechanism Examples
  9. Results
  10. Optimality of Common Lotteries
  11. Partial Converse
  12. Optimal Mechanisms
  13. Implementation of Common Lotteries
  14. Characterizing Feasible Mechanisms
  15. Common Ordinal Preferences
  16. ...and 18 more sections

Key Result

Theorem 1

Suppose $1/F$ is convex. For any feasible direct mechanism $a$, there exists a feasible common lottery $\tilde{a}(\cdot)$ with $\bm{s}(a)=\bm{s}(\tilde{a})$. In particular, for any designer objective function $V$ and agent mass $D$, there exists an optimal mechanism that is a common lottery.

Figures (8)

  • Figure 1: First-best and common lottery examples
  • Figure 2: Screening mechanism examples
  • Figure 3: Insufficiency of local IC constraints for feasibility.
  • Figure 4: Optimal Mechanism Example
  • Figure 5: Perturbation for Partial Converse
  • ...and 3 more figures

Theorems & Definitions (29)

  • Definition 1
  • Theorem 1
  • Theorem 2
  • Proposition 1
  • Corollary 1
  • Proposition 2
  • Proposition 3: MON
  • Proposition 4
  • Proposition 5
  • Corollary 2
  • ...and 19 more