Optimal Truncation in Matching Markets
AbstractSince no stable matching mechanism can induce truth-telling as a dominant strategy for all participants, there is often room in matching markets for strategic misrepresentation (Roth ). In this paper we study a natural form of strategic misrepresentation: reporting a truncation of one's true preference list. Roth and Rothblum  prove an important but abstract result: in certain symmetric, incomplete information settings, agents on one side of the market (“the women”) optimally submit some truncation of their true preference lists. In this paper we put structure on this truncation, both in symmetric and general settings, when agents must submit preference lists to the Men-Proposing Deferred Acceptance Algorithm. We first characterize each woman's truncation payoffs in an incomplete information setting in terms of the distribution of her achievable mates. The optimal degree of truncation can be substantial: we prove that in a uniform setting, the optimal degree of truncation for an individual woman goes to 100% of her list as the market size grows large, when other women are truthful. In this setting, we demonstrate the existence of an equilibrium where all agents use truncation strategies. Compared to truthful reporting, in any equilibrium in truncation strategies, welfare diverges for men and women: women prefer the truncation equilibrium, while men would prefer that participants truthfully report. In a general environment, we show that the less risk averse a player, the greater the degree of her optimal truncation. Finally, when correlation in preferences increases, players should truncate less. While several recent papers have focused on the limits of strategic manipulation, our results serve as a reminder that without the pre-conditions ensuring truthful reporting, even in settings where agents have little information, the potential for manipulation can be significant.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2013.49.
Date of creation: May 2013
Date of revision:
Matching Markets; Truncation;
Find related papers by JEL classification:
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- D47 - Microeconomics - - Market Structure and Pricing - - - Market Design
- D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-16 (All new papers)
- NEP-CTA-2013-06-16 (Contract Theory & Applications)
- NEP-DEM-2013-06-16 (Demographic Economics)
- NEP-GTH-2013-06-16 (Game Theory)
- NEP-MIC-2013-06-16 (Microeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Elliott Peranson & Alvin E. Roth, 1999.
"The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design,"
American Economic Review, American Economic Association,
American Economic Association, vol. 89(4), pages 748-780, September.
- Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," NBER Working Papers 6963, National Bureau of Economic Research, Inc.
- Coles, Peter Andrew & Levine, Phillip B. & Roth, Alvin E. & Cawley, John & Niederle, Muriel & Siegfried, John J., 2010.
"The Job Market for New Economists: A Market Design Perspective,"
5343168, Harvard University Department of Economics.
- Peter Coles & John Cawley & Phillip B. Levine & Muriel Niederle & Alvin E. Roth & John J. Siegfried, 2010. "The Job Market for New Economists: A Market Design Perspective," Journal of Economic Perspectives, American Economic Association, vol. 24(4), pages 187-206, Fall.
- Ehlers, Lars & Masso, Jordi, 2007. "Incomplete information and singleton cores in matching markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 136(1), pages 587-600, September.
- Hideo Konishi & M. Ãœnver, 2006.
"Games of Capacity Manipulation in Hospital-intern Markets,"
Social Choice and Welfare, Springer,
Springer, vol. 27(1), pages 3-24, August.
- Hideo Konishi & M. Utku Unver, 2001. "Games of Capacity Manipulation in Hospital-Intern Markets," Boston College Working Papers in Economics, Boston College Department of Economics 515, Boston College Department of Economics, revised 31 Jul 2002.
- Robin S. Lee & Michael Schwarz, 2009. "Interviewing in Two-Sided Matching Markets," NBER Working Papers 14922, National Bureau of Economic Research, Inc.
- Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, Econometric Society, vol. 67(1), pages 21-44, January.
- Dzierzawa, Michael & OmÃ©ro, Marie-JosÃ©, 2000. "Statistics of stable marriages," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 287(1), pages 321-333.
- Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 77(1), pages 197-204, November.
- Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, American Economic Association, vol. 99(3), pages 608-27, June.
- Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 277-288, August.
- Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, American Economic Association, vol. 84(4), pages 992-1044, September.
- Janine Balter & Michela Rancan & Olena Senyuta, 2014. "Truncation in the Matching Markets and Market Ineffciency," RSCAS Working Papers, European University Institute 2014/04, European University Institute.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (barbara racah).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.