Credible implementation

The theory of implementation abounds with mechanisms with intricate systems of rewards and punishments off-the-equilibrium path. Generally, it is not in the designer's best interest to go through with the reward/punishment in the "subgame" arising from some disequilibrium play. This would make the mechanism's outcome function non-credible. We define a notion of credible implementation and, in the domain of exchange economies, we show that (a) the non-dictatorial Pareto correspondence can be credibly implemented (b) there is no credibly implementable Pareto-efficient and individually rational social choice rule (SCR) and (c) there is no credibly implementable Pareto-efficient and envy-free SCR. We derive necessary and sufficient conditions for credible implementability of SCR. The main implication is that it is sub-optimal for the designer to be endowed with "too much" information about the economy. Finally, we show that the negative results persist under weaker credibility requirements. (c) 2005 Elsevier Inc. All rights reserved.