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Relationships between Non-Bossiness and Nash Implementability

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  • Hideki Mizukami

    ()
    (Faculty of Economics, Toyama University)

  • Takuma Wakayama

    ()
    (Graduate School of Economics, Osaka University)

Abstract

We explore the relationships between non-bossiness and Nash implementability. We provide a new domain-richness condition, weak monotonic closedness, and prove that on weakly monotonically closed domains, non-bossiness together with individual monotonicity is equivalent to monotonicity, a necessary condition for Nash implementation. The result shows an impossibility of Nash implementation in all economies except pure public goods economies, in the sense that it indicates that in all economies except pure public goods economies, it is impossible to implement bossy social choice functions in Nash equilibria, which embody the characteristics inherent in those economies.

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Bibliographic Info

Paper provided by Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP) in its series Discussion Papers in Economics and Business with number 05-33.

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Length: 12 pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:osk:wpaper:0533

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Web page: http://www.econ.osaka-u.ac.jp/
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Keywords: Non-Bossiness; Individual Monotonicity; Monotonicity; Weak Monotonic Closedness.;

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  1. Shigehiro Serizawa, 1997. "Strategy-proof and individually rational social choice functions for public good economies," Economic Theory, Springer, vol. 9(2), pages 379-380.
  2. Ju, Biung-Ghi, 2004. "Continuous selections from the Pareto correspondence and non-manipulability in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 573-592, August.
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  7. Svensson, Lars-Gunnar & Larsson, Bo, 2000. "Strategy-Proof and Nonbossy Allocation of Indivisible Goods and Money," Working Papers 2000:11, Lund University, Department of Economics.
  8. Lin Zhou, 1990. "Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies," Cowles Foundation Discussion Papers 954, Cowles Foundation for Research in Economics, Yale University.
  9. Miyagawa, Eiichi, 2001. "House Allocation with Transfers," Journal of Economic Theory, Elsevier, vol. 100(2), pages 329-355, October.
  10. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  11. Schummer, James, 2000. "Eliciting Preferences to Assign Positions and Compensation," Games and Economic Behavior, Elsevier, vol. 30(2), pages 293-318, February.
  12. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer, vol. 16(4), pages 557-567.
  14. Takamiya, Koji, 2001. "Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 201-213, March.
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