  Envy-freeness and Pareto Efficiency are two major goals in welfare economics.
The existence of an allocation that satisfies both conditions has been studied
for a long time. Whether items are indivisible or divisible, it is impossible
to achieve envy-freeness and Pareto Efficiency ex post even in the case of two
people and two items. In contrast, in this work, we prove that, for any
cardinal utility functions (including complementary utilities for example) and
for any number of items and players, there always exists an ex ante mixed
allocation which is envy-free and Pareto Efficient, assuming the allowable
assignments are closed under swaps, i.e. if given a legal assignment, swapping
any two players' allocations produces another legal assignment. The problem
remains open in the divisible case.
  We also investigate the communication complexity for finding a Pareto
Efficient and envy-free allocation.
