A New Approach to Fair Distribution of Welfare

TL;DR

This paper introduces a novel solution concept for transferable-utility profit-sharing games that ensures efficiency, fairness, and decomposability, addressing limitations of existing mechanisms in joint decision-making scenarios.

Contribution

The paper proposes a new solution concept that simultaneously satisfies efficiency, fairness, and decomposition properties, with proven existence and uniqueness under submodularity.

Findings

The new solution concept exists and is unique under submodularity.

It satisfies key properties that previous solutions fail to meet simultaneously.

Applicable to settings like the Shared-Rental problem.

Abstract

We consider transferable-utility profit-sharing games that arise from settings in which agents need to jointly choose one of several alternatives, and may use transfers to redistribute the welfare generated by the chosen alternative. One such setting is the Shared-Rental problem, in which students jointly rent an apartment and need to decide which bedroom to allocate to each student, depending on the student's preferences. Many solution concepts have been proposed for such settings, ranging from mechanisms without transfers, such as Random Priority and the Eating mechanism, to mechanisms with transfers, such as envy free solutions, the Shapley value, and the Kalai-Smorodinsky bargaining solution. We seek a solution concept that satisfies three natural properties, concerning efficiency, fairness and decomposition. We observe that every solution concept known (to us) fails to satisfy at least one of the three properties. We present a new solution concept, designed so as to satisfy the three properties. A certain submodularity condition (which holds in interesting special cases such as the Shared-Rental setting) implies both existence and uniqueness of our solution concept.