Undominated Nash Implementation in Bounded Mechanisms

We study implementation in undominated Nash equilibrium by bounded mechanisms. (An undominated Nash equilibrium is a Nash equilibrium in which no agent uses a weakly dominated strategy. A mechanism is bounded if every dominated strategy is dominated by some undominated strategy.) We identify necessary conditions and sufficient conditions for such implementation. These conditions are satisfied in virtually all economic environments, and are also satisfied by interesting correspondences from the social choice literature. For economic settings, we provide a particularly simple implementing mechanism for which the undominated equilibrium outcomes coincide with those obtained from the iterative elimination of weakly dominated strategies