Egalitarian Equivalent Allocations over a Single Good

This paper studies efficient and egalitarian allocations over a single heterogeneous and infinitely divisible good. We prove the existence of such allocations using only measure-theoretic arguments. Under the additional assumption of complete information, we identify a sufficient condition on agents' preferences that makes it possible to apply the Pazner-Schmeidler rule for uniquely selecting an efficient egalitarian equivalent allocation. Finally, we exhibit a simple procedure that implements the Pazner-Schmeidler selection in a subgame-perfect equilibrium.