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Games with capacity manipulation: incentives and Nash equilibria

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  • Antonio Romero-Medina
  • Matteo Triossi

Abstract

Studying the interactions between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and sufficient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal and intern-optimal stable rules. We then introduce generalized games of manipulation in which hospitals move first and state their capacities, and interns are subsequently assigned to hospitals using a sequential mechanism. In this setting, we first consider stable revelation mechanisms and introduce conditions guaranteeing the stability of the outcome. Next, we prove that every stable non-revelation mechanism leads to unstable allocations, unless restrictions on the preferences of the agents are introduced. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Antonio Romero-Medina & Matteo Triossi, 2013. "Games with capacity manipulation: incentives and Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 701-720, September.
    • Handle: RePEc:spr:sochwe:v:41:y:2013:i:3:p:701-720
    DOI: 10.1007/s00355-012-0703-1
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    2. Romero-Medina, Antonio & Triossi, Matteo, 2013. "Acyclicity and singleton cores in matching markets," Economics Letters, Elsevier, vol. 118(1), pages 237-239.
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    8. Kojima Fuhito, 2007. "When Can Manipulations be Avoided in Two-Sided Matching Markets? -- Maximal Domain Results," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, September.
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    14. Marilda Sotomayor, 2003. "Reaching the core of the marriage market through a non-revelation matching mechanism," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 241-251, December.
    15. Romero-Medina, Antonio & Triossi, Matteo, 2014. "Non-revelation mechanisms in many-to-one markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 624-630.
    16. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
    17. Alejandra Mizala & Pilar Romaguera & Sebastian Gallegos, 2010. "Public-Private Wage Gap In Latin America (1999-2007): A Matching Approach," Documentos de Trabajo 268, Centro de Economía Aplicada, Universidad de Chile.
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    1. Ehlers, Lars, 2010. "Manipulation via capacities revisited," Games and Economic Behavior, Elsevier, vol. 69(2), pages 302-311, July.
    2. Assaf Romm, 2014. "Implications of capacity reduction and entry in many-to-one stable matching," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 851-875, December.
    3. Inácio Bó & C.-Philipp Heller, 2017. "Strategic schools under the Boston mechanism revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 545-572, March.
    4. Romero-Medina, Antonio & Triossi, Matteo, 2013. "Acyclicity and singleton cores in matching markets," Economics Letters, Elsevier, vol. 118(1), pages 237-239.
    5. Tello Benjamín, 2017. "Stability of Equilibrium Outcomes under Deferred Acceptance: Acyclicity and Dropping Strategies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 17(2), pages 1-9, June.
    6. Antonio Romero-Medina & Matteo Triossi, 2021. "Two-sided strategy-proofness in many-to-many matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 105-118, March.
    7. Akahoshi, Takashi, 2014. "Singleton core in many-to-one matching problems," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 7-13.
    8. Hagen, Martin, 2022. "Tradable immigration quotas revisited," Journal of Public Economics, Elsevier, vol. 208(C).

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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