Two-stage Stochastic Matching and Pricing with Applications to Ride Hailing

58 Pages Posted: 22 Jul 2020 Last revised: 25 Jan 2022

See all articles by Yiding Feng

Yiding Feng

Microsoft Corporation - Microsoft Research New England

Rad Niazadeh

University of Chicago - Booth School of Business

Amin Saberi

Stanford University - Department of Management Science & Engineering

Date Written: May 29, 2020

Abstract

Matching and pricing are two critical levers in two-sided marketplaces to connect demand and supply. The platform can produce more efficient matching and pricing decisions by batching the demand requests. We initiate the study of the two-stage stochastic matching problem, with or without pricing, to enable the platform to make improved decisions in a batch with an eye toward the imminent future demand requests. This problem is motivated in part by applications in online marketplaces such as ride hailing platforms.

We design online competitive algorithms for vertex-weighted (or unweighted) two-stage stochastic matching for maximizing supply efficiency, and two-stage joint matching and pricing for maximizing market efficiency. In the former problem, using a randomized primal-dual algorithm applied to a family of "balancing" convex programs, we obtain the optimal 3/4 competitive ratio against the optimum offline benchmark. Using a factor revealing program and connections to submodular optimization, we improve this ratio against the optimum online benchmark to (1−1/e+1/e^2) ≈ 0.767 for the unweighted and 0.761 for the weighted case. In the latter problem, we design optimal 1/2-competitive joint pricing and matching algorithm by borrowing ideas from the ex-ante prophet inequality literature. We also show an improved (1−1/e)-competitive algorithm for the special case of demand efficiency objective using the correlation gap of submodular functions. Finally, we complement our theoretical study by using DiDi’s ride-sharing dataset for Chengdu city and numerically evaluating the performance of our proposed algorithms in practical instances of this problem.

Keywords: Online matching, Ride hailing, Pricing

Suggested Citation

Feng, Yiding and Niazadeh, Rad and Saberi, Amin, Two-stage Stochastic Matching and Pricing with Applications to Ride Hailing (May 29, 2020). Chicago Booth Research Paper No. 20-28, Available at SSRN: https://ssrn.com/abstract=3613755 or http://dx.doi.org/10.2139/ssrn.3613755

Yiding Feng

Microsoft Corporation - Microsoft Research New England ( email )

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

Rad Niazadeh (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S Woodlawn Ave
Chicago, IL 60637

HOME PAGE: http://radniazadeh.github.io/

Amin Saberi

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

473 Via Ortega
Stanford, CA 94305-9025
United States

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