The Role of the Common Prior in Robust Implementation

Abstract

We consider the role of the common prior for robust implementation in an environment with interdependent values. Specifically, we investigate a model of public good provision which allows for negative and positive informational externalities. In the corresponding direct mechanism, the agents' reporting strategies are strategic complements with negative informational externalities and strategic substitutes with positive informational externalities.

We derive the necessary and sufficient conditions for robust implementation in common prior type spaces and contrast this with our earlier results without the common prior. In the case of strategic complements the necessary and sufficient conditions for robust implementation do not depend on the existence of a common prior. In contrast, with strategic substitutes, the implementation conditions are much weaker under the common prior assumption.

Keywords: Common prior, Correlated equilibrium, Ex post equilibrium, Mechanism design, Robust implementation, Rationalizability, Strategic complements, Strategic substitutes, Uniqueness

JEL Classification: C79, D82