On the existence of Pareto Efficient and envy-free allocations

• 成果类型: Article
• 署名作者: Cole, Richard; Tao, Yixin
• 署名单位: New York University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2021.105207
• 发表日期: 2021
• 关键词: Pareto Efficient; Envy-free; Fair allocation; communication complexity

摘要

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. (c) 2021 Elsevier Inc. All rights reserved.