Implementation in Undominated Strategies: A Look at Bounded Mechanisms

This paper examines the impact of placing natural restrictions on the mechanisms considered for implementation problems. It is shown that if all mechanisms are considered and preferences satisfy a basic condition, then any social choice correspondence can be implemented in undominated strategies. An example points out that the strength of this result derives from the use of mechanisms with questionable features. In part of the message space the agent who announces the highest integer is rewarded. This sort of "tail-chasing" construction, common in the constructive proofs of the literature, is used to assure that undesired strategy combinations do not form an equilibrium. If such mechanisms are ruled out, then the social choice correspondences which can be implemented in undominated strategies satisfy an incentive compatibility type condition called strategy-resistence. For social choice functions this is equivalent to strategy-proofness. This contrast suggests that this issue should be examined as it applies to other solution concepts used in implementation theory. The last portion of the paper begins to explore the issue as it relates to Nash implementation and undominated Nash implementation.