TY - GEN
T1 - Matchings under preferences
T2 - 20th ACM Conference on Economics and Computation, EC 2019
AU - Chen, Jiehua
AU - Skowron, Piotr
AU - Sorge, Manuel
N1 - Publisher Copyright:
© 2019 Association for Computing Machinery.
PY - 2019/6/17
Y1 - 2019/6/17
N2 - We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness requires that a matching must be stable in the classic sense, even if the agents slightly change their preferences. Near stability, on the other hand, imposes that a matching must become stable (again, in the classic sense) provided the agents are willing to adjust their preferences a bit. Both of our concepts are quantitative; together they provide means for a fine-grained analysis of the stability of matchings. Moreover, our concepts allow the exploration of trade-offs between stability and other criteria of social optimality, such as the egalitarian cost and the number of unmatched agents. We investigate the computational complexity of finding matchings that implement certain predefined trade-offs. We provide a polynomial-time algorithm that, given agent preferences, returns a socially optimal robust matching, and we prove that finding a socially optimal and nearly stable matching is computationally hard.
AB - We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness requires that a matching must be stable in the classic sense, even if the agents slightly change their preferences. Near stability, on the other hand, imposes that a matching must become stable (again, in the classic sense) provided the agents are willing to adjust their preferences a bit. Both of our concepts are quantitative; together they provide means for a fine-grained analysis of the stability of matchings. Moreover, our concepts allow the exploration of trade-offs between stability and other criteria of social optimality, such as the egalitarian cost and the number of unmatched agents. We investigate the computational complexity of finding matchings that implement certain predefined trade-offs. We provide a polynomial-time algorithm that, given agent preferences, returns a socially optimal robust matching, and we prove that finding a socially optimal and nearly stable matching is computationally hard.
KW - Approximation algorithms
KW - Concepts of stability
KW - Exact algorithms
KW - NP-hardness
KW - Parameterized complexity analysis
KW - Stable matchings
UR - https://www.scopus.com/pages/publications/85069039376
U2 - 10.1145/3328526.3329555
DO - 10.1145/3328526.3329555
M3 - Conference contribution
AN - SCOPUS:85069039376
T3 - ACM EC 2019 - Proceedings of the 2019 ACM Conference on Economics and Computation
SP - 41
EP - 59
BT - ACM EC 2019 - Proceedings of the 2019 ACM Conference on Economics and Computation
PB - Association for Computing Machinery, Inc
Y2 - 24 June 2019 through 28 June 2019
ER -