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.
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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
- 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-GTH-2013-06-16 (Game Theory)
- NEP-MIC-2013-06-16 (Microeconomics)
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- Hideo Konishi & M. Utku Unver, 2001.
"Games of Capacity Manipulation in Hospital-Intern Markets,"
Boston College Working Papers in Economics
515, Boston College Department of Economics, revised 31 Jul 2002.
- Hideo Konishi & M. Ünver, 2006. "Games of Capacity Manipulation in Hospital-intern Markets," Social Choice and Welfare, Springer, vol. 27(1), pages 3-24, August.
- Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
- Dzierzawa, Michael & Oméro, Marie-José, 2000. "Statistics of stable marriages," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 321-333.
- Ehlers, Lars & Masso, Jordi, 2007. "Incomplete information and singleton cores in matching markets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 587-600, 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.
- 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, vol. 89(4), pages 748-780, September.
- Robin S. Lee & Michael Schwarz, 2009. "Interviewing in Two-Sided Matching Markets," NBER Working Papers 14922, National Bureau of Economic Research, Inc.
- 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, vol. 84(4), pages 992-1044, September.
- Coles, Peter Andrew & Cawley, John & Levine, Phillip B. & Roth, Alvin E. & Siegfried, John J. & Niederle, Muriel, 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.
- Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
- Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-27, June.
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