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Virtual Demand and Stable Mechanisms

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  • Jan Christoph Schlegel

Abstract

We study conditions for the existence of stable, strategy-proof mechanisms in a many-to-one matching model with salaries. Workers and firms want to match and agree on the terms of their match. Firms demand different sets of workers at different salaries. Workers have preferences over different firm-salary combinations. Workers' preferences are monotone in salaries. We show that for this model, a descending auction mechanism is the only candidate for a stable mechanism that is strategy-proof for workers. Moreover, we identify a maximal domain of demand functions for firms, such that the mechanism is stable and strategy-proof. In the special case, where demand functions are generated by quasi-linear profit functions, our domain reduces to the domain of demand functions under which workers are gross substitutes for firms. We provide two versions of the results for the quasi-linear case. One for a discrete model, where salaries are restricted to discrete units and one for a continuous model, where salaries can take on arbitrary positive numbers. More generally, we show that several celebrated results (the existence of a worker-optimal stable allocation, the rural hospitals theorem, the strategy-proofness of the worker-optimal stable mechanism) generalize from the discrete to the continuous model.

Suggested Citation

  • Jan Christoph Schlegel, 2016. "Virtual Demand and Stable Mechanisms," Cahiers de Recherches Economiques du Département d'économie 16.11, Université de Lausanne, Faculté des HEC, Département d’économie.
  • Handle: RePEc:lau:crdeep:16.11
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    References listed on IDEAS

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    1. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    2. Hirata, Daisuke & Kasuya, Yusuke, 2017. "On stable and strategy-proof rules in matching markets with contracts," Journal of Economic Theory, Elsevier, vol. 168(C), pages 27-43.
    3. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    4. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    5. Schlegel, Jan Christoph, 2015. "Contracts versus salaries in matching: A general result," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 552-573.
    6. Hirata, Daisuke & Kasuya, Yusuke, 2014. "Cumulative offer process is order-independent," Economics Letters, Elsevier, vol. 124(1), pages 37-40.
    7. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    8. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186-219.
    9. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    10. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-440, June.
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    Cited by:

    1. Schlegel, Jan Christoph, 2022. "The structure of equilibria in trading networks with frictions," Theoretical Economics, Econometric Society, vol. 17(2), May.
    2. Jagadeesan, Ravi, 2018. "Lone wolves in infinite, discrete matching markets," Games and Economic Behavior, Elsevier, vol. 108(C), pages 275-286.
    3. Jagadeesan, Ravi & Kominers, Scott Duke & Rheingans-Yoo, Ross, 2018. "Strategy-proofness of worker-optimal matching with continuously transferable utility," Games and Economic Behavior, Elsevier, vol. 108(C), pages 287-294.
    4. Schlegel, Jan Christoph, 2020. "Equivalent choice functions and stable mechanisms," Games and Economic Behavior, Elsevier, vol. 123(C), pages 41-53.
    5. Ravi Jagadeesan & Scott Duke Kominers & Ross Rheingans-Yoo, 2020. "Lone wolves in competitive equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 215-228, August.

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    More about this item

    Keywords

    Matching with contracts; Matching with salaries; Gross Substitutes; Virtual Demand;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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