DOUBLE IMPLEMENTATION IN NASH AND UNDOMINATED NASH EQUILIBRIA

This paper studies the issue of designing mechanisms that are applicable to a wide class of individual behavior in exchange economies with both “goods” and “bads.” We propose a mechanism such that for each possible preference profile, both the set of Nash equilibrium allocations and the set of undominated Nash equilibrium allocations coincide with the set of allocations that are optimal according to some social choice correspondence (SCC). Such a mechanism is said to “doubly” implement the SCC in Nash equilibria and undominated Nash equilibria. We show that in a large class of economies with ar least three agents, Maskin’s [Nash equilibrium and welfare optimality, mimeo, M.I.T., 1977] condition of monotonicity is necessary and sufficient for double implementation. Journal of Economic Literature Classification Numbers: C72, D51, D78. © 1993 Academic Press, Inc.