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Monotonic extensions on economic domains

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Author Info
William Thomson () (Department of Economics, University of Rochester, Rochester, NY 14627, USA)

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Abstract

The property of "monotonicity" is necessary, and in many contexts, sufficient, for a solution to be Nash implementable (Maskin 1977). In this paper, we follow Sen (1995) and evaluate the extent to which a solution may fail monotonicity by identifying the minimal way in which it has to be enlarged so as to satisfy the property. We establish a general result relating the "minimal monotonic extensions" of the intersection and the union of a family of solutions to the minimal monotonic extensions of the members of the family. We then calculate the minimal monotonic extensions of several solutions in a variety of contexts, such as classical exchange economies, with either individual endowments or a social endowment, economies with public goods, and one-commodity economies in which preferences are single-peaked. For some of the examples, very little is needed to recover monotonicity, but for others, the required enlargement is quite considerable, to the point that the distributional objective embodied in the solution has to be given up altogether.

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Publisher Info
Article provided by Springer in its journal Review of Economic Design.

Volume (Year): 4 (1999)
Issue (Month): 1 ()
Pages: 13-33
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Handle: RePEc:spr:reecde:v:4:y:1999:i:1:p:13-33

Note: Received: 21 September 1996 / Accepted: 17 August 1998
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Related research
Keywords: Maskin-monotonicity; Nash-implementation; minimal monotonic extension; fair allocation;

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation

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  1. BOCHET, Olivier & MANIQUET, Franois, 2006. "Virtual Nash implementation with admissible support," CORE Discussion Papers 2006084, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  2. Olivier Bochet, 2007. "Implementation of the Walrasian correspondence: the boundary problem," International Journal of Game Theory, Springer, vol. 36(2), pages 301-316, October. [Downloadable!] (restricted)
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  3. Pablo Amoros, 2008. "Unequivocal Majority and Maskin-Monotonicity," Working Papers 2008-3, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center. [Downloadable!]
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  4. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  5. Claus-Jochen Haake & Bettina Klaus, 2009. "Monotonicity and Nash implementation in matching markets with contracts," Economic Theory, Springer, vol. 41(3), pages 393-410, December. [Downloadable!] (restricted)
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  6. Veiga, Helena & Vorsatz, Marc, 2006. "Price Manipulation in an Experimental Asset Market," Research Memoranda 024, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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  7. İpek Özkal-Sanver & M. Sanver, 2006. "Nash implementation via hyperfunctions," Social Choice and Welfare, Springer, vol. 26(3), pages 607-623, June. [Downloadable!] (restricted)
  8. Orhan Erdem & M. Sanver, 2005. "Minimal monotonic extensions of scoring rules," Social Choice and Welfare, Springer, vol. 25(1), pages 31-42, October. [Downloadable!] (restricted)
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