  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.
