Competitive equilibrium for almost all incomes

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Abstract

Competitive equilibrium from equal incomes (CEEI) is a well-known rule for fair allocation of resources among agents with different preferences. It has many advantages, among them is the fact that a CEEI allocation is both Pareto efficient and envy-free. However, when the resources are indivisible, a CEEI allocation might not exist even when there are two agents and a single item. In contrast to this discouraging non-existence result, Babaioff, Nisan and Talgam-Cohen (2017) recently suggested a new and more encouraging approach to allocation of indivisible items: instead of insisting that the incomes be equal, they suggest to look at the entire space of possible incomes, and check whether there exists a competitive equilibrium for almost all income-vectors (CEFAI) - All income-space except a subset of measure zero. They show that a CEFAI exists when there are at most 3 items, or when there are 4 items and two agents. They also show that when there are 5 items and two agents there might not exist a CEFAI. They leave open the cases of 4 items with three or four agents. This paper presents a new way to implement a CEFAI, as a subgame-perfect equilibrium of a sequential game. This new implementation allows us both to offer much simpler solutions to the known cases (at most 3 items, and 4 items with two agents), and to prove that a CEFAI exists even in the much more difficult case of 4 items and three agents. Moreover, we prove that a CEFAI might not exist with 4 items and four agents. Thus, this paper completes the characterization of CEFAI for monotone preferences.

Original languageEnglish
Title of host publication17th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2018
Pages1267-1275
Number of pages9
StatePublished - 2018
Event17th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2018 - Stockholm, Sweden
Duration: 10 Jul 201815 Jul 2018

Publication series

NameProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Volume2

Conference

Conference17th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2018
Country/TerritorySweden
CityStockholm
Period10/07/1815/07/18

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering

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