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The B.E. Journal of Theoretical Economics

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On Nash Implementability in Allotment Economies under Domain Restrictions with Indifference

Ahmed Doghmi
  • Corresponding author
  • University of Rabat, Mohammadia School of Engineering, the QSM Laboratory, Avenue Ibn Sina B.P. 765 Agdal, 10100 Rabat, Morocco
  • Center for Research in Economics and Management (UMR CNRS 6211), University of Caen, 19 Rue Claude Bloch 14032 Caen, Cedex, France
  • Email:
Published Online: 2016-06-01 | DOI: https://doi.org/10.1515/bejte-2015-0091

Abstract

In this paper we give a full characterization of Nash implementability of social choice correspondences (SCCs) in allotment economies on preference domains with private values and different types of indifference. We focus on single-peaked/single-plateaued preferences with worst indifferent allocations, single-troughed preferences and single-troughed preferences with best indifferent allocations. We begin by introducing a weak variant of no-veto power, called I-weak no-veto power, which form together with unanimity and a stronger version of Maskin monotonicity a sufficient condition for Nash implementation in general environment. We apply this result to the above preference domains and we prove that any SCC that has full range is Nash implementable if and only if it satisfies Maskin monotonicity. We examine the implementability of some well-known correspondences. We give examples of SCCs that are monotonic in the unrestricted domains and also monotonic in our setup, and we provide exemples of SCCs that are not monotonic in the unrestricted domains, but monotonic and therefore Nash implementable in our context. Finally, we give examples of SCCs that are not monotonic in the restricted domains and also not monotonic in our area, and therefore not Nash implementable.

Keywords: allotment economies; domain restrictions with indifference; nash implementation

JEL: C72; D71

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About the article

Published Online: 2016-06-01

Published in Print: 2016-06-01



Citation Information: The B.E. Journal of Theoretical Economics, ISSN (Online) 1935-1704, ISSN (Print) 2194-6124, DOI: https://doi.org/10.1515/bejte-2015-0091. Export Citation

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