Dividing goods or bads under additive utilities

TL;DR

This paper compares two fair division rules, Egalitarian Equivalent and Competitive Equilibrium with Equal Incomes, for dividing goods and bads, highlighting their advantages and limitations in different scenarios.

Contribution

It provides a comparative analysis of division rules for goods and bads, including an axiomatic characterization of the Competitive rule under additive utilities.

Findings

Competitive division is resource monotonic for goods.

For bads, the Competitive rule is multivalued and computationally harder.

The paper offers an axiomatic foundation for the Competitive rule.

Abstract

We compare the Egalitarian Equivalent and the Competitive Equilibrium with Equal Incomes rules to divide a bundle of goods (heirlooms) or a bundle of bads (chores). For goods the Competitive division fares better, as it is Resource Monotonic, and makes it harder to strategically misreport preferences. But for bads, the Competitive rule, unlike the Egalitarian one, is multivalued, harder to compute, and admits no continuous selection. We also provide an axiomatic characterization of the Competitive rule based on the simple formulation of Maskin Monotonicity under additive utilities.