Price Discovery in Waiting Lists

55 Pages Posted: 22 Aug 2022 Last revised: 24 Aug 2022

See all articles by Itai Ashlagi

Itai Ashlagi

Stanford University - Department of Management Science & Engineering

Jacob Leshno

Chicago Booth

Pengyu Qian

Boston University - Questrom School of Business

Amin Saberi

Stanford University - Department of Management Science & Engineering

Date Written: August 23, 2022

Abstract

Waiting lists offer agents a choice between types of items with associated nonmonetary prices given by required waiting times. These nonmonetary prices are endogenously determined by a tâtonnement-like price discovery process: an item's price increases when an agent queues for it, and decreases when an item arrives and is assigned to a queuing agent. We show that a waiting list's price discovery process generates waiting times that fluctuate around market-clearing prices. We bound the loss from these price fluctuations by the granularity of price adjustments. The technical approach and intuition for the results relies on a connection between price adjustments in the waiting list and the stochastic gradient descent optimization algorithm. We further show that this simple price discovery process is asymptotically optimal if the granularity of price adjustments optimally balances between the adaptivity and the rigidity of the price discovery process.

Keywords: Price discovery, waiting lists, assignment problem, market-clearing prices, tâtonnement, stochastic gradient descent

JEL Classification: D47, E3, D61

Suggested Citation

Ashlagi, Itai and Leshno, Jacob and Qian, Pengyu and Saberi, Amin, Price Discovery in Waiting Lists (August 23, 2022). Available at SSRN: https://ssrn.com/abstract=4192003 or http://dx.doi.org/10.2139/ssrn.4192003

Itai Ashlagi

Stanford University - Department of Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

Jacob Leshno (Contact Author)

Chicago Booth ( email )

5807 S. Woodlawn Ave
Chicago, IL 60610
United States

Pengyu Qian

Boston University - Questrom School of Business ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

Amin Saberi

Stanford University - Department of Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

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