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Group strategy-proofness in private good economies without money: matching, division and house allocation

Author

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  • Salvador Barberà
  • Dolors Berga
  • Bernardo Moreno

Abstract

We observe that three salient solutions to matching, division and house allocation problems are not only (partially) strategy-proof, but (partially) group strategy-proof as well, in appropriate domains of definition. That is the case for the Gale-Shapley mechanism, the uniform rule and the top trading cycle solution, respectively. We embed these three types of problems into a general framework. We then notice that the three rules, as well as many others, do share a common set of properties, which together imply their (partial) group strategy-proofness. This proves that the equivalence between individual and group strategy-proofness in all these cases is not a fortuitous event, but results from the structure of the functions under consideration.

Suggested Citation

  • Salvador Barberà & Dolors Berga & Bernardo Moreno, 2014. "Group strategy-proofness in private good economies without money: matching, division and house allocation," Working Papers 773, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:773
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    References listed on IDEAS

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    1. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
    2. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    3. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
    4. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    5. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    6. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    7. Mark A. Satterthwaite & Hugo Sonnenschein, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(4), pages 587-597.
    8. Masso, Jordi & Neme, Alejandro, 2001. "Maximal Domain of Preferences in the Division Problem," Games and Economic Behavior, Elsevier, vol. 37(2), pages 367-387, November.
    9. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    10. Kojima, Fuhito, 2010. "Impossibility of stable and nonbossy matching mechanisms," Economics Letters, Elsevier, vol. 107(1), pages 69-70, April.
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    Cited by:

    1. William Thomson, 2016. "Non-bossiness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 665-696, October.
    2. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2016. "Group Strategy-Proofness in Private Good Economies," American Economic Review, American Economic Association, vol. 106(4), pages 1073-1099, April.

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    More about this item

    Keywords

    matching; division; house allocation; strategy-proofness; group strategy-proofness; group monotonicity; non-bossiness;
    All these keywords.

    JEL classification:

    • 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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