Nash implementation and double implementation: Equivalence theorems
In the case of implementation in Nash equilibria or of implementation in undominated Nash equilibria mechanisms have been proposed. However, for the mechanisms proposed for Nash equilibria, the set of undominated Nash equilibrium outcomes may be strictly smaller than the set of Nash equilibrium outcomes. In such a case, there is no guarantee that a mechanism designed for Nash implementation of a given social choice correspondence will implement it if the agents do not use weakly dominated strategies. In this paper, the author considers the design of mechanisms for which both the set of Nash equilibrium outcomes and the set of undominated Nash equilibrium outcomes coincide with the set of outcomes that are optimal according to a given social choice correspondence. He provides a characterization of correspondences implementable in Nash equilibria for at least three agents. In the two-agent case, another characterization is proposed.
scientific article; zbMATH DE number 1330500
scientific article