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Non-Monetary Dynamic Allocation to Agents with Unit Demand

46 Pages Posted: 4 May 2017 Last revised: 29 Jun 2017

Nick Arnosti

Columbia Business School - Decisions, Risk, and Operations Division

Peng Shi

University of Southern California - Marshall School of Business

Date Written: February 13, 2017

Abstract

We consider a setting in which agents and items match dynamically over time. We show that repeated independent lotteries with unlimited entry (which are commonly used in practice) encourage agents to enter many lotteries, and may result in low match value.

We consider three alternate mechanisms: allowing agents to save unused tickets, limiting agents to entering at most one lottery, and allocating developments using a waiting list. We show that these three mechanisms are equivalent: for each agent, the probability of matching and expected value conditioned on matching are identical.

Compared to a repeated lottery, these mechanisms result in higher-quality matches for matched agents. However, in some cases, a repeated lottery is more likely to match agents with the worst outside options, and thus may outperform the other mechanisms in terms of utilitarian welfare. We discuss the implications of these findings for two systems in New York City that currently use a repeated lottery: the allocation of affordable housing and of discounted tickets to broadway shows.

JEL Classification: C78, D82, D44

Suggested Citation

Arnosti, Nick and Shi, Peng, Non-Monetary Dynamic Allocation to Agents with Unit Demand (February 13, 2017). Columbia Business School Research Paper No. 17-52. Available at SSRN: https://ssrn.com/abstract=2963178

Nick Arnosti (Contact Author)

Columbia Business School - Decisions, Risk, and Operations Division ( email )

3022 Broadway
New York, NY 10027
United States

Peng Shi

University of Southern California - Marshall School of Business ( email )

701 Exposition Blvd
Los Angeles, CA 90089
United States

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