Filling Positions Without Transfers: Screening on Outside Options

2026-02-11

AI Summary

This study addresses the problem of allocating hierarchical positions to maximize a designer’s preference over the number of acceptances when monetary transfers are infeasible and agents possess private outside options. Leveraging mechanism design theory and probabilistic decomposition techniques, the paper characterizes the feasible structure of agents’ participation probabilities and identifies the form of the optimal randomized allocation mechanism. The analysis reveals that under a general condition on the distribution of outside options, offering a uniform lottery to all agents is optimal; otherwise, an optimal mechanism must provide a menu of differentiated lotteries to screen agents effectively. This result departs from the conventional screening paradigm that relies on type reporting, demonstrating that efficient screening can be achieved through random allocation alone in environments without monetary transfers.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• screening
• outside options
• mechanism design
• lotteries
• vertical differentiation

Innovation

• mechanism design without transfers
• outside options
• screening
• lottery mechanisms
• participation probability decomposition