TY - GEN
T1 - A Tight Negative Example for MMS Fair Allocations
AU - Feige, Uriel
AU - Sapir, Ariel
AU - Tauber, Laliv
N1 - Publisher Copyright: © 2022, Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - We consider the problem of allocating indivisible goods to agents with additive valuation functions. Kurokawa, Procaccia and Wang [JACM, 2018] present instances for which every allocation gives some agent less than her maximin share. We present such examples with larger gaps. For three agents and nine items, we design an instance in which at least one agent does not get more than a 3940 fraction of her maximin share. Moreover, we show that there is no negative example in which the difference between the number of items and the number of agents is smaller than six, and that the gap (of 140 ) of our example is worst possible among all instances with nine items. For n≥ 4 agents, we show examples in which at least one agent does not get more than a 1-1n4 fraction of her maximin share. In the instances designed by Kurokawa, Procaccia and Wang, the gap is exponentially small in n. Our proof techniques extend to allocation of chores (items of negative value), though the quantitative bounds for chores are different from those for goods. For three agents and nine chores, we design an instance in which the MMS gap is 143.
AB - We consider the problem of allocating indivisible goods to agents with additive valuation functions. Kurokawa, Procaccia and Wang [JACM, 2018] present instances for which every allocation gives some agent less than her maximin share. We present such examples with larger gaps. For three agents and nine items, we design an instance in which at least one agent does not get more than a 3940 fraction of her maximin share. Moreover, we show that there is no negative example in which the difference between the number of items and the number of agents is smaller than six, and that the gap (of 140 ) of our example is worst possible among all instances with nine items. For n≥ 4 agents, we show examples in which at least one agent does not get more than a 1-1n4 fraction of her maximin share. In the instances designed by Kurokawa, Procaccia and Wang, the gap is exponentially small in n. Our proof techniques extend to allocation of chores (items of negative value), though the quantitative bounds for chores are different from those for goods. For three agents and nine chores, we design an instance in which the MMS gap is 143.
UR - http://www.scopus.com/inward/record.url?scp=85124279005&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-030-94676-0_20
DO - https://doi.org/10.1007/978-3-030-94676-0_20
M3 - منشور من مؤتمر
SN - 9783030946753
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 355
EP - 372
BT - Web and Internet Economics - 17th International Conference, WINE 2021, Proceedings
A2 - Feldman, Michal
A2 - Fu, Hu
A2 - Talgam-Cohen, Inbal
PB - Springer Science and Business Media B.V.
T2 - 17th International Conference on Web and Internet Economics, WINE 2021
Y2 - 14 December 2021 through 17 December 2021
ER -