On the existence of Pareto Efficient and envy-free allocations

Richard Cole, Yixin Tao

Research output: Contribution to journalArticlepeer-review


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 satisfy an anonymity property. The problem remains open in the divisible case. We also investigate the communication complexity for finding a Pareto Efficient and envy-free allocation.

Original languageEnglish (US)
Article number105207
JournalJournal of Economic Theory
StatePublished - Apr 2021


  • Communication complexity
  • Envy-free
  • Fair allocation
  • Pareto Efficient

ASJC Scopus subject areas

  • Economics and Econometrics


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