TY - GEN
T1 - Competitive equilibrium for almost all incomes
AU - Segal-Halevi, Erel
N1 - Publisher Copyright: © 2018 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85054688529&partnerID=8YFLogxK
M3 - منشور من مؤتمر
SN - 9781510868083
T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
SP - 1267
EP - 1275
BT - 17th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2018
T2 - 17th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2018
Y2 - 10 July 2018 through 15 July 2018
ER -