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Optimal Truncation in Matching Markets

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  • Peter Coles

    (Harvard Business School)

  • Ran Shorrer

    (Harvard University and Harvard Business School)

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    Abstract

    Since 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 [25]). In this paper we study a natural form of strategic misrepresentation: reporting a truncation of one's true preference list. Roth and Rothblum [28] 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 Info

    Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2013.49.

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    Date of creation: May 2013
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    Handle: RePEc:fem:femwpa:2013.49

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    Keywords: Matching Markets; Truncation;

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    References

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    1. 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.
    2. 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," Scholarly Articles 5343168, Harvard University Department of Economics.
    3. 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.
    4. 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.
    5. Robin S. Lee & Michael Schwarz, 2009. "Interviewing in Two-Sided Matching Markets," NBER Working Papers 14922, National Bureau of Economic Research, Inc.
    6. 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.
    7. Dzierzawa, Michael & Oméro, Marie-José, 2000. "Statistics of stable marriages," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 287(1), pages 321-333.
    8. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 77(1), pages 197-204, November.
    9. 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.
    10. 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.
    11. 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.
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    Cited by:
    1. 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.

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