Full implementation of social choice functions in dominant strategies

We consider the classical mechanism design problem of fully implementing social choice functions in dominant strategies in settings where monetary payments are allowed and the utility functions are quasi-linear. We consider both the general question of full implementation by indirect mechanisms and the special case of full implementation by incentive compatible direct revelation mechanisms. For the general case of full implementation by indirect mechanisms, we prove that one can restrict attention to incentive compatible augmented revelation mechanisms, in which the type space of each agent is a subset of the set of her possible bids and truthful reporting is a dominant strategy equilibrium. When the type spaces of the agents are finite, we give a complete characterization of the set of social choice functions that can be fully implemented in dominant strategies. For the case that one restricts to incentive compatible direct revelation mechanisms, we show that an adaption of the well-known negative cycle criterion for partial implementability also characterizes the social choice functions that are fully implementable.