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Faulty Nash Implementation in Exchange Economies with Single-peaked Preferences

Author

Listed:
  • Ahmed Doghmi

    () (Strategic Interaction Group, Max Planck Institute of Economics, Jena, Germany)

  • Abderrahmane Ziad

    () (Center for Research in Economics and Management, University of Caen, France)

Abstract

In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one hand and we extend theorems 1 and 2 of Doghmi and Ziad (2008a) to bounded rationality environments, on the other. We identify weak versions of the k-no veto power condition, in conjunction with unanimity and variants of k-monotonicity, are sufficient for implementability in k- Fault Tolerant Nash equilibria (k-FTNE). In addition, these new conditions are stable by intersection which makes it possible to check directly the k-FTNE implementability of the social choice correspondences. We apply these results to exchange economies with single -peaked preferences, to ?nite allocation problems, and to equilibrium theory. Firstly, we note that our conditions are satis?ed by all monotonic solutions contrary to Eliaz's results (2002). Secondly, in exchange economy when preferences are single-peaked, the k-monotonicity is sufficient for the k-FTNE implementation for the correspondences and both necessary and sufficient for the functions. However, the results are negatives for the no-monotonic solutions.

Suggested Citation

  • Ahmed Doghmi & Abderrahmane Ziad, 2009. "Faulty Nash Implementation in Exchange Economies with Single-peaked Preferences," Jena Economic Research Papers 2009-073, Friedrich-Schiller-University Jena.
  • Handle: RePEc:jrp:jrpwrp:2009-073
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    Keywords

    Faulty Nash implementation; Bounded rationality; Exchange economies; Single-peaked preferences;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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