Designing Approximately Optimal Search on Matching Platforms

44 Pages Posted: 28 May 2021 Last revised: 16 Aug 2021

See all articles by Nicole Immorlica

Nicole Immorlica

Microsoft Research

Brendan Lucier

Microsoft Research

Vahideh Manshadi

Yale School of Management

Alexander Wei

University of California, Berkeley

Date Written: May 20, 2021

Abstract

We study the design of a decentralized two-sided matching market in which agents’ search is guided by the platform. There are finitely many agent types, each with (potentially random) preferences drawn from known type-specific distributions. Equipped with knowledge of these distributions, the platform guides the search process by determining the meeting rate between each pair of types from the two sides. Focusing on symmetric pairwise preferences in a continuum model, we first characterize the unique stationary equilibrium that arises given a feasible set of meeting rates. We then introduce the platform’s optimal directed search problem, which involves optimizing meeting rates to maximize equilibrium social welfare. We first show that incentive issues arising from congestion and cannibalization make the design problem fairly intricate. Nonetheless, we develop an efficiently computable search design whose corresponding equilibrium achieves at least 1/4 the social welfare of the optimal design. In fact, our construction always recovers at least 1/4 the first-best social welfare, where agents’ incentives are disregarded. Our directed search design is simple and easy-to-implement, as its corresponding bipartite graph consists of disjoint stars. Furthermore, our design implies the platform can substantially limit choice and yet induce an equilibrium with an approximately optimal welfare. Finally, we show that approximation is likely the best we can hope for by establishing that the problem of designing optimal directed search is NP-hard to even approximate beyond a certain constant factor.

Keywords: search, matching platforms, congestion, market design

Suggested Citation

Immorlica, Nicole and Lucier, Brendan and Manshadi, Vahideh and Wei, Alexander, Designing Approximately Optimal Search on Matching Platforms (May 20, 2021). Available at SSRN: https://ssrn.com/abstract=3850164 or http://dx.doi.org/10.2139/ssrn.3850164

Nicole Immorlica

Microsoft Research ( email )

One Memorial Drive, 14th Floor
Cambridge, MA 02142
United States

Brendan Lucier

Microsoft Research ( email )

One Memorial Drive, 14th Floor
Cambridge, MA 02142
United States

Vahideh Manshadi (Contact Author)

Yale School of Management ( email )

135 Prospect Street
P.O. Box 208200
New Haven, CT 06520-8200
United States

Alexander Wei

University of California, Berkeley

Soda Hall
Berkeley, CA 94720
United States

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