On the existence of Pareto Efficient and envy-free allocations

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 indivisible or divisible, it is impossible to achieve envy-freeness ex post even the case people items. In contrast, this work, we prove that, any cardinal utility functions (including complementary utilities example) number players, there always exists ante mixed which envy-free Efficient, assuming allowable assignments satisfy anonymity property. problem remains open divisible case. We also investigate communication complexity finding Efficient allocation.