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Preference Revelation Games and Strong Cores of Allocation Problems with Indivisibilities

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  • Koji Takamiya
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    Abstract

    This paper studies the incentive compatibility of solutions to generalized indivisible good allocation problems introduced by Sonmez (1999), which contain the well-known marriage problems (Gale and Shapley, 1962) and the housing markets (Shapley and Scarf, 1974) as special cases. In particular, I consider the vulnerability to manipulation of solutions that are individually rational and Pareto optimal. By the results of Sonmez (1999) and Takamiya (2003), any individually rational and Pareto optimal solution is strategy-proof if and only if the strong core correspondence is essentially single-valued, and the solution is a strong core selection. Given this fact, this paper examines the equilibrium outcomes of the preference revelation games when the strong core correspondence is not necessarily essentially single-valued. I show that for the preference revelation games induced by any solution which is individually rational and Pareto optimal, the set of strict strong Nash equilibrium outcomes coincides with the strong core. This generalizes one of the results by Shin and Suh (1996) obtained in the context of the marriage probelms. Further, I examine the other preceding results proved for the marriage problems (Alcalde, 1996; Shin and Suh, 1996; Sonmez, 1997) to find that none of those results are generalized to the general model.

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    File URL: http://www.iser.osaka-u.ac.jp/library/dp/2006/DP0651.pdf
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    Paper provided by Institute of Social and Economic Research, Osaka University in its series ISER Discussion Paper with number 0651.

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    Date of creation: Mar 2006
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    Handle: RePEc:dpr:wpaper:0651

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    1. José Alcalde, 1995. "Implementation of Stable Solutions to Marriage Problems," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 1995-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    2. Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer, Springer, vol. 17(2), pages 101-27.
    3. Shin, Sungwhee & Suh, Sang-Chul, 1996. "A mechanism implementing the stable rule in marriage problems," Economics Letters, Elsevier, vol. 51(2), pages 185-189, May.
    4. Thomson, William, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 51(3), pages 447-60, July.
    5. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, 9.
    6. Ehud Kalai, 1978. "A Group Incentive Compatible Mechanism Yielding Core Allocation," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 329, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, Econometric Society, vol. 67(3), pages 677-690, May.
    8. Koji Takamiya, 2003. "On strategy-proofness and essentially single-valued cores: A converse result," Social Choice and Welfare, Springer, Springer, vol. 20(1), pages 77-83.
    9. 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.
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