Faulty Nash Implementation in Exchange Economies with Single-peaked Preferences
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.
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