Monotonic extensions on economic domains |
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Authors: | William Thomson |
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Institution: | (1) Department of Economics, University of Rochester, Rochester, NY 14627, USA (e-mail: wth2@db1.cc.rochester.edu) , US |
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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.
Received: 21 September 1996 / Accepted: 17 August 1998 |
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Keywords: | : Maskin-monotonicity Nash-implementation minimal monotonic extension fair allocation |
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