Efficient investments in the implementation problem

Abstract

This paper identifies a condition for an efficient social choice rule to be fully implementable when we take into account investment efficiency. To do so, we extend the standard implementation problem to include endogenous ex ante and ex post investments. In our problem, the social planner aims to achieve efficiency in every equilibrium of a dynamic game in which agents strategically make investments before and after playing the mechanism. Our main theorem shows that a novel condition commitment-proofness is sufficient and necessary for an efficient social choice rule to be implementable in subgame-perfect equilibria. The availability of ex post investments is crucial in our model: there is no social choice rule that is efficient and implementable in subgame-perfect equilibria without ex post investments. We also show that our positive result continues to hold in the incomplete information setting.