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Ordinally Bayesian Incentive Compatible Stable Matching

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  • Dipjyoti Majumdar

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study incentive issues related to the two-sided one-to-one stable matching problem after weakening the notion of strategy-proofness to Ordinal Bayesian Incentive Compatibility (OBIC). Under OBIC, truthtelling is required to maximize expected utility of every agent, expected utility being computed with respect to the agent's prior and under the assumption that everybody else is also telling the truth. We show that when preferences are unrestricted there exists no matching procedure that is both stable and OBIC. Next preferences are restricted to the case where remaining single is the worst alternative for every agent. We show that in this case, if agents have uniform priors the stable matching generated by the "deferred acceptance algorithms" are OBIC. However, for generic priors there are no procedures that are both stable and OBIC even with restricted preferences.

Suggested Citation

  • Dipjyoti Majumdar, 2003. "Ordinally Bayesian Incentive Compatible Stable Matching," Working Papers hal-00242988, HAL.
    • Handle: RePEc:hal:wpaper:hal-00242988
    Note: View the original document on HAL open archive server: https://hal.science/hal-00242988
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    References listed on IDEAS

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    1. d’ASPREMONT, C. & PELEG, B., 1986. "Ordinal Bayesian incentive compatible representations of committees," LIDAM Discussion Papers CORE 1986042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Ehlers, Lars, 2004. "In search of advice for participants in matching markets which use the deferred-acceptance algorithm," Games and Economic Behavior, Elsevier, vol. 48(2), pages 249-270, August.
    3. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    4. Roth, Alvin E., 1989. "Two-sided matching with incomplete information about others' preferences," Games and Economic Behavior, Elsevier, vol. 1(2), pages 191-209, June.
    5. Alcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 417-435, May.
    6. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    7. Dipjyoti Majumdar & Arunava Sen, 2003. "Ordinally Bayesian incentive-compatible voting schemes," Discussion Papers 03-01, Indian Statistical Institute, Delhi.
    8. 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.
    9. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    10. Roth, Alvin E & Vande Vate, John H, 1991. "Incentives in Two-Sided Matching with Random Stable Mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 31-44, January.
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    Cited by:

    1. 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.
    2. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    3. M. Bumin Yenmez, 2013. "Incentive-Compatible Matching Mechanisms: Consistency with Various Stability Notions," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 120-141, November.
    4. Joana Pais, 2008. "Random matching in the college admissions problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 99-116, April.
    5. Pais, Joana, 2008. "Incentives in decentralized random matching markets," Games and Economic Behavior, Elsevier, vol. 64(2), pages 632-649, November.
    6. Debasis Mishra, 2014. "A Foundation for Dominant Strategy Voting Mechanisms," ISER Discussion Paper 0916, Institute of Social and Economic Research, Osaka University.
    7. Ehlers, Lars & Massó, Jordi, 2015. "Matching markets under (in)complete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 295-314.
    8. Bikhchandani, Sushil, 2017. "Stability with one-sided incomplete information," Journal of Economic Theory, Elsevier, vol. 168(C), pages 372-399.

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    More about this item

    Keywords

    Stable matching; Incentives; Strategy-proofness; Marriage stable; Incitation; Manipulabilité;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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