Correlated information, mechanism design and informational rents

Crémer and McLean (Econometrica 56 (1988) 1247-1258) obtain a sufficient and necessary condition for full surplus extraction in Bayesian-Nash equilibrium-the rank condition, which McAfee and Reny (Econometrica 60(2) (1992) 395-421) later generalize for continuous type spaces. This paper shows that, if the principal does not know how noisy is the agent's signal-or equivalently, when signals available to an agent can be ranked by Blackwell's informativeness and, an agent's informativeness is independent of others' information, the rank condition fails to hold. Conversely, when rank condition fails and informational rents are left to an agent, the model can be interpreted as if, the principal were uncertain about the informativeness of the agent's signal.