Matching Markets with Chores

TL;DR

This paper extends fair division concepts to matching markets involving chores and mixed manna, establishing equilibrium equivalences and generalizing known results from goods to chores.

Contribution

It introduces the first extension of fair division to matching markets with chores and mixed manna, and shows equilibrium equivalences in these settings.

Findings

Extended fair division results to chores and mixed manna in matching markets.

Proved equivalence between earnings-based and pricing-based equilibria.

Generalized known results from goods to chores and mixed manna.

Abstract

The fair division of chores, as well as mixed manna (goods and chores), has received substantial recent attention in the fair division literature; however, ours is the first paper to extend this research to matching markets. Indeed, our contention is that matching markets are a natural setting for this purpose, since the manna that fit into the limited number of hours available in a day can be viewed as one unit of allocation. We extend several well-known results that hold for goods to the settings of chores and mixed manna. In addition, we show that the natural notion of an earnings-based equilibrium, which is more natural in the case of all chores, is equivalent to the pricing-based equilibrium given by Hylland and Zeckhauser for the case of goods.