Implementation and Partial Provability

We extend implementation theory by allowing the social choice function to depend on more than just the pro le of preferences of the agents and by allowing agents to support their statements with hard evidence. We show that a simple condition on the evidence structure which is necessary for the implementation of a social choice function f when the preferences of the agents are state independent is also sufficient for implementation for any preferences (including state dependent) if the social planner can perform small monetary transfers and there are at least three players. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under an additional boundedness assumption. In both cases, transfers only occur off the equilibrium path. Finally, in the special but important case of allocation problems, under weak conditions, f can be implemented in a perfect information game with at least two players and no transfers. In all cases, the use of evidence enables implementation which is robust in the sense that the social planner needs very little information about the preferences, beliefs, and evidence of the agents and the agents need little information about each others' preferences.