Fair allocation of indivisible goods among two agents

One must allocate a finite set of indivisible goods among two agents without monetary compensation. We impose Pareto-efficiency, anonymity, a weak notion of no-envy, a welfare lower bound based on each agent’s ranking of the sets of goods, and a monotonicity property relative to changes in agents’ preferences. We prove that there is a rule satisfying these axioms. If there are three goods, it is the only rule, with one of its subcorrespondences, satisfying each fairness axiom and not discriminating between goods. Further, we confirm the clear gap between these economies and those with more than two agents.