Maximin Fair Allocation of Indivisible Items Under Cost Utilities

Sirin Botan, Angus Ritossa, Mashbat Suzuki, Toby Walsh

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.