۱- Introduction

۲- Model

۳- Example

۴- Main results

۵- Without ex post investments

۶- Discussions

۷- Concluding remarks

References

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.

Introduction

The literature on implementation theory has identified which social choice rules can be fully implemented under various solution concepts and informational assumptions. Here, full implementation means that the set of all equilibrium outcomes of the mechanism coincides with the set of outcomes specified by the social choice rule. Although this is a strong requirement, the literature has shown rather permissive results: for example, under complete information and quasi-linear utility, any social choice rule is implementable in subgame-perfect equilibria (Moore and Repullo, 1988; Maskin and Tirole, 1999).1 In the implementation problem, however, the problem of investment incentives has not been fully examined. In many real-life applications such as auctions and the provision of public goods, there are opportunities for agents to invest in the outcomes of the mechanism (Tan, 1992; Bag, 1997; Arozamena and Cantillon, 2004). When agents strategically invest before participating in a mechanism, the positive results implied by implementation theory may be threatened. That is, although the mechanism implements efficient allocations at the market clearing stage, it may not necessarily induce efficient ex ante investments in equilibrium. In particular, even when there is an efficient investment equilibrium, we may not be able to rule out other inefficient equilibria, which is a concern of the full implementation problem.