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Strategy-proofness and essentially single-valued cores revisited

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  • EHLERS, Lars
Abstract
We consider general allocation problems with indivisibilities where agents' preferences possibly exhibit externalities. In such contexts many different core notions were proposed. One is the gamma-core whereby blocking is only allowed via allocations where the non-blocking agents receive their endowment. We show that if there exists an allocation rule satisfying ‘individual rationality’, ‘efficiency’, and ‘strategy-proofness’, then for any problem for which the gamma-core is non-empty, the allocation rule must choose a gamma-core allocation and all agents are indifferent between all allocations in the gamma-core. We apply our result to housing markets, coalition formation and networks.

Suggested Citation

  • EHLERS, Lars, 2014. "Strategy-proofness and essentially single-valued cores revisited," Cahiers de recherche 2014-02, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:2014-02
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    File URL: http://hdl.handle.net/1866/10925
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    References listed on IDEAS

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    1. Parkash Chander & Henry Tulkens, 2006. "The Core of an Economy with Multilateral Environmental Externalities," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 153-175, Springer.
    2. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 457-488.
    3. Jaramillo, Paula & Manjunath, Vikram, 2012. "The difference indifference makes in strategy-proof allocation of objects," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1913-1946.
    4. Jinpeng Ma, 1998. "Strategic Formation of Coalitions," Discussion Papers 1225, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
    6. Alcalde-Unzu, Jorge & Molis, Elena, 2011. "Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms," Games and Economic Behavior, Elsevier, vol. 73(1), pages 1-16, September.
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    9. Koji Takamiya, 2003. "On strategy-proofness and essentially single-valued cores: A converse result," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(1), pages 77-83.
    10. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
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    12. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    13. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
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    16. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    17. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 203-215, June.
    18. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
    19. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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    Cited by:

    1. María Haydée Fonseca‐Mairena & Matteo Triossi, 2023. "Notes on marriage markets with weak externalities," Bulletin of Economic Research, Wiley Blackwell, vol. 75(4), pages 860-868, October.
    2. Zhang, Jun, 2023. "Strategy-proof allocation with outside option," Games and Economic Behavior, Elsevier, vol. 137(C), pages 50-67.
    3. Hong, Miho & Park, Jaeok, 2022. "Core and top trading cycles in a market with indivisible goods and externalities," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    4. Fonseca-Mairena, María Haydée & Triossi, Matteo, 2022. "Incentives and implementation in allocation problems with externalities," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    5. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2018. "Housing market models with consumption externalities," CSEF Working Papers 500, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. Afacan, Mustafa Oğuz & Hu, Gaoji & Li, Jiangtao, 2024. "Housing markets since Shapley and Scarf," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    7. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2020. "Shapley and Scarf housing markets with consumption externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(5), pages 1481-1514, September.

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    More about this item

    Keywords

    General allocation problems; Externalities; Strategy-proofness; Gamma-core;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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