Mathematical Culture and Thought

Mathematical Culture and Thought

Matching Mechanisms: A Brief View

Document Type : Review

Authors
M. Pourpouneh 1
R. Ramezanian 2
1 Department of Mathematical Sciences, Sharif University of Technology, Iran
2 Pure Mathematics Department, Ferdowsi University of Mashhad, Iran
10.30504/mct.2022.322
Abstract
Matching  mechanisms are essential in the economic behavior of human society.  It   can easily be observed in marriage, kidney transplant allocation, allocation of tasks, etc.  The main topic of the problem of matching  mechanism design  is to bring the two parties together while the greatest benefit occurs. The two parties should not have any reason to contradict in revealing their preferences. The purpose of this paper is to introduce  the reader to the topic of designing mechanisms and, in particular, adaptation mechanisms.
Keywords
mechanism design
matching
stable marriage
deferred acceptance algorithm
top trading cycle algorithm
Subjects
[1] Abdulkadiroğlu, A., Sönmez, T., House allocation with existing tenants, J. Econom. Theory,
88 (1999), 233-260.
[2] Akbarpour, M., Shengwu, L., Oveis Gharan, Sh., Dynamic matching market design (2014),
available at https://arxiv.org/abs/1402.3643.
[3] Babaioff, M., Immorlica, N., Kempe, D., Kleinberg, R., Online auctions and generalized
secretary problems, ACM SIGecom Exchanges, 7 (2008), 7.
[4] Gale, D., Shapley, L. S., College admissions and the stability of marriage, Amer. Math.
Monthly, 69 (1962), 9-15.
[5] Irving, R. W., An efficient algorithm for the “stable roommates” problem, Journal of Algorithms,
6 (1985), 577-595.
[6] Liu, Q., Mailath, G. J., Postlewaite, A., Samuelson, L., Stable matching with incomplete
information, Econometrica, 82 (2014), 541-587.
[7] Roth, A. E., Two-sided matching with incomplete information about others’ preferences,
Games Econom. Behav., 1 (1989), 191-209.
[8] Roth, A. E., The evolution of the labor market for medical interns and residents: a case
study in game theory, Journal of Political Economy, 92 (1984), 991-1016.
[9] Roth, A. E., Sonmez, T., Utku Unver, M., Kidney exchange, National Bureau of Economic
Research, 2003. doi: 10.3386/w10002

  • Receive Date 16 January 2017
  • Revise Date 23 February 2017
  • Accept Date 23 February 2017
  • Publish Date 20 February 2022