Fair Allocation with Money: What is Your Objective?

TL;DR

This paper compares different models of monetary transfers in indivisible item allocation, analyzing their objectives and bounds to understand fair and efficient distribution methods.

Contribution

It systematically compares various monetary transfer models and explores the relationships between their bounds and optimization objectives.

Findings

Different transfer models have distinct optimization goals.

Upper and lower bounds vary across models and objectives.

Insights into fair allocation with monetary transfers are provided.

Abstract

When allocating indivisible items, there are various ways to use monetary transfers for eliminating envy. Particularly, one can apply a balanced vector of transfer payments, or charge each agent a positive amount, or -- contrarily -- give each agent a positive amount as a ``subsidy''. In each model, one can aim to minimize the amount of payments used; this aim translates into different optimization objectives in each setting. This note compares the various models, and the relations between upper and lower bounds for these objectives.