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Implementations of the Nash solution based on its Walrasian characterization

By Walter Trockel

Abstract

The present paper provides three different support results for the Nash bargaining solution of $n$-person bargaining games. First, for any bargaining game there is defined a non-cooperative game in strategic form, whose unique Nash equilibrium induces a payoff vector that coincides with the Nash solution of the bargaining game. Next this game is modified in such a way that the unique Nash equilibrium that supports the Nash solution is even in dominant strategies. After that an $n$-stage game in extensive form is presented whose unique subgame perfect equilibrium supports the Nash solution of the bargaining game. Finally, the support results are shown to induce implementation results in the sense of mechanism theory.Nash solution, Nash-implementation, Mechanism, Walrasian equilibrium.

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