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Ordinally Bayesian Incentive Compatible Stable Matchings

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  • Dipjyoti Majumdar

    ()
    (Department of Economics, Concordia University)

Abstract

We study incentive issues related to 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 the expected utility of every agent, expected utility being computed with respect to the agent’s prior beliefs 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 then the stable matchings generated by “deferred acceptance algorithms” are OBIC. However, for generic priors there are no matching procedures that are both stable and OBIC even with restricted preferences.

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Bibliographic Info

Paper provided by Concordia University, Department of Economics in its series Working Papers with number 05001.

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Length: 26 pages
Date of creation: Aug 2003
Date of revision:
Handle: RePEc:crd:wpaper:05001

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Keywords: stable matching; incentives; strategy-proofness;

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References

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  1. Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents 1994-1, Nobel Prize Committee.
  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. d’ASPREMONT, C. & PELEG, B., 1986. "Ordinal Bayesian incentive compatible representations of committees," CORE Discussion Papers 1986042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Dipjyoti Majumdar & Arunava Sen, 2003. "Ordinally Bayesian incentive-compatible voting schemes," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 03-01, Indian Statistical Institute, New Delhi, India.
  5. Alcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer, vol. 4(3), pages 417-35, May.
  6. 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.
  7. 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.
  8. Roth, Alvin E & Vande Vate, John H, 1991. "Incentives in Two-Sided Matching with Random Stable Mechanisms," Economic Theory, Springer, vol. 1(1), pages 31-44, January.
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Cited by:
  1. EHLERS, Lars & MASSÓ, Jordi, 2007. "Matching Markets under (In)complete Information," Cahiers de recherche 01-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Pais, Joana, 2008. "Incentives in decentralized random matching markets," Games and Economic Behavior, Elsevier, vol. 64(2), pages 632-649, November.
  3. Joana Pais, 2008. "Random matching in the college admissions problem," Economic Theory, Springer, vol. 35(1), pages 99-116, April.
  4. M. Bumin Yenmez, 2013. "Incentive-Compatible Matching Mechanisms: Consistency with Various Stability Notions," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 120-41, November.

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