Revenue Maximization in Choice-Based Matching Markets

TL;DR

This paper introduces approximation algorithms for revenue maximization in choice-based matching markets with arbitrary pairwise rewards, addressing both customized and inclusive models and overcoming challenges posed by non-submodular rewards.

Contribution

It provides the first constant-factor approximation guarantees for reward maximization in general pairwise reward matching markets, using novel linear relaxations and analytical techniques.

Findings

Achieved constant-factor approximation guarantees for revenue maximization.

Developed novel linear relaxations and analytical tools for non-submodular rewards.

Addressed both customized and inclusive models in matching markets.

Abstract

The primary contribution of this paper resides in devising constant-factor approximation guarantees for revenue maximization in two-sided matching markets, under general pairwise rewards. A major distinction between our work and state-of-the-art results in this context (Ashlagi et al., 2022; Torrico et al., 2023) is that, for the first time, we are able to address reward maximization, reflected by assigning each customer-supplier pair an arbitrarily-valued reward. The specific type of performance guarantees we attain depends on whether one considers the customized model or the inclusive model. The fundamental difference between these settings lies in whether the platform should display to each supplier all selecting customers, as in the inclusive model, or whether the platform can further personalize this set, as in the customized model. Technically speaking, our algorithmic approach and its analysis revolve around presenting novel linear relaxations, leveraging convex stochastic orders, employing approximate dynamic programming, and developing tailor-made analytical ideas. In both models considered, these ingredients allow us to overcome the lack of submodularity and subadditivity that stems from pairwise rewards, plaguing the applicability of existing methods.