Manipulability in matching markets: conflict and coincidence of interests

We study comparative statics of manipulations by women in the men-proposing deferred acceptance mechanism in the two-sided one-to-one marriage market. We prove that if a group of women weakly successfully manipulates or employs truncation strategies, then all other women weakly benefit and all men are weakly harmed. We show that these results do not appropriately generalize to the many-to-one college admissions model.

[1]  Alvin E. Roth.  Deferred acceptance algorithms: history, theory, practice, and open questions , 2008, Int. J. Game Theory.

[2]  Lars Ehlers,et al.  Truncation Strategies in Matching Markets , 2008, Math. Oper. Res..

[3]  A. Roth.  Stability and Polarization of Interests in Job Matching , 1984 .

[4]  Alvin E. Roth,et al.  Sorority Rush as a Two-Sided Matching Mechanism , 1991 .

[5]  U. Rothblum,et al.  Truncation Strategies in Matching Markets-in Search of Advice for Participants , 1999 .

[6]  Harry R. Lewis,et al.  Review of "Mariages stables et leur relations avec d'autre problèmes combinatoires: introduction à l'analyze mathématique des algorithmes" by Donald E. Knuth. Les Presses de l'Université de Montréal. , 1978, SIGA.

[7]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[8]  David A. Freedman,et al.  Machiavelli and the Gale-Shapley Algorithm , 1981 .

[9]  Jinpeng Ma,et al.  The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP) , 2010, Games Econ. Behav..

[10]  Parag A. Pathak,et al.  Appendix to "Incentives and Stability in Large Two-Sided Matching Markets" , 2009 .

[11]  Alvin E. Roth,et al.  The College Admissions Problem Revisited , 1989 .

[12]  Alvin E. Roth,et al.  Incentives in two-sided matching with random stable mechanisms , 1991 .

[13]  A. Roth.  Misrepresentation and stability in the marriage problem , 1984 .

[14]  A. Roth.  The college admissions problem is not equivalent to the marriage problem , 1985 .

[15]  Alvin E. Roth,et al.  The Economics of Matching: Stability and Incentives , 1982, Math. Oper. Res..

[16]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[17]  V. Crawford.  Comparative statics in matching markets , 1991 .

[18]  Alvin E. Roth,et al.  Conflict and Coincidence of Interest in Job Matching: Some New Results and Open Questions , 1985, Math. Oper. Res..