Ordinal and cardinal solution concepts for two-sided matching

TL;DR

This paper introduces a unified cardinal framework for analyzing two-sided matching problems, comparing models with and without transfers, and introduces the concept of no-trade matchings to understand transfer effects.

Contribution

It provides a novel cardinal characterization of matching solutions and the concept of no-trade matchings to analyze transfer roles in matching models.

Findings

Cardinal solutions for transferable and nontransferable utility models are characterized.

The concept of no-trade matching clarifies when transfers impact outcomes.

Comparison between matching models with and without transfers is made transparent.

Abstract

We characterize solutions for two-sided matching, both in the transferable and in the nontransferable-utility frameworks, using a cardinal formulation. Our approach makes the comparison of the matching models with and without transfers particularly transparent. We introduce the concept of a no-trade matching to study the role of transfers in matching. A no-trade matching is one in which the availability of transfers do not affect the outcome.