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.