Nash Implementation and Uncertain Renegotiation

Abstract

This paper studies Nash implementation when the outcomes of the mechanism can be renegotiated among the agents but the planner does not know the renegotiation function that they will use. We character-ize the social objectives that can be implemented in Nash equilibrium when the same mechanism must work for every admissible renegoti-ation function. The constrained Walrasian correspondence, the core correspondence, and the Pareto-efficient and envy-free correspondence satisfy the necessary and sufficient conditions for this form of imple-mentation if and only if free-disposal of the commodities is allowed. The uniform rule, on the other hand, is not Nash implementable for some admissible renegotiations functions. Key-words: Implementation theory, Nash equilibrium, renegotiation functio