High Welfare Matching Markets via Descending Price

TL;DR

This paper analyzes a descending-price auction mechanism for two-sided matching markets, demonstrating its welfare guarantees and extending its analysis to various models, including those with costs and hypergraph matchings.

Contribution

It provides the first formal analysis of the Marshallian Match descending-price mechanism, establishing welfare bounds and extending results to complex market models.

Findings

Marshallian Match achieves constant price of anarchy with positive valuations.

The mechanism extends to models with information costs and hypergraph matchings.

Main welfare guarantees for negative valuations remain an open problem.

Abstract

We consider design of monetary mechanisms for two-sided matching. Mechanisms in the tradition of the deferred acceptance algorithm, even in variants incorporating money, tend to focus on the criterion of stability. Instead, in this work we seek a simple auction-inspired mechanism with social welfare guarantees. We consider a descending-price mechanism called the Marshallian Match, proposed (but not analyzed) by Waggoner and Weyl (2019). When all values for potential matches are positive, we show the Marshallian Match with a "rebate" payment rule achieves constant price of anarchy. This result extends to models with costs for acquiring information about one's values, and also to matching on hypergraphs. With possibly-negative valuations, which capture e.g. job markets, the problem becomes harder. We introduce notions of approximate stability and show that they have beneficial welfare implications. However, the main problem of proving constant factor welfare guarantees in "ex ante stable equilibrium" remains open.