Maximin Fair Allocation of Indivisible Items under Cost Utilities

TL;DR

This paper investigates fair division of indivisible items with cost utilities, proving existence of maximin fair share allocations for small groups and special preference structures, and exploring strategyproof mechanisms.

Contribution

It establishes the existence of MMS allocations under cost utilities for three agents and laminar preferences for any number of agents, advancing fair division theory.

Findings

MMS allocations always exist for three agents with cost utilities.

MMS allocations can be guaranteed for any number of agents with laminar set approvals.

Explores the possibility of strategyproof mechanisms for MMS allocations.

Abstract

We study the problem of fairly allocating indivisible goods among a set of agents. Our focus is on the existence of allocations that give each agent their maximin fair share--the value they are guaranteed if they divide the goods into as many bundles as there are agents, and receive their lowest valued bundle. An MMS allocation is one where every agent receives at least their maximin fair share. We examine the existence of such allocations when agents have cost utilities. In this setting, each item has an associated cost, and an agent's valuation for an item is the cost of the item if it is useful to them, and zero otherwise. Our main results indicate that cost utilities are a promising restriction for achieving MMS. We show that for the case of three agents with cost utilities, an MMS allocation always exists. We also show that when preferences are restricted slightly further--to what we call laminar set approvals--we can guarantee MMS allocations for any number of agents. Finally, we explore if it is possible to guarantee each agent their maximin fair share while using a strategyproof mechanism.