Optimal use of correlated information in mechanism design when full surplus extraction may be impossible

We study the mechanism design problem when the principal can condition the agent's transfers on the realization of ex post signals that are correlated with the agent's types. Crémer and McLean [Econometrica 53(1985) 345–361; 56(1988) 1247–1257], McAfee and Reny [Econometrica 60(2)(1992) 395–421], and Riordan and Sappington [J. Econ. Theory, 45(1988) 189–199] studied situations where the signals are such that full surplus can be extracted from every agent type. We study optimal utilization of the signals when there are fewer signals than types and the Riordan and Sappington conditions do not always hold. For some special cases, we show the level of surplus that can be extracted, and identify the agent types who obtain rent.