Implementation in an interdependent value framework

• Monotone outcome functions are ex post Nash implementable under interdependent values.
• Monotonicity is with respect to an agent-specific partial order on social alternatives.
• Efficient outcome functions are monotone under lattice-theoretic assumptions.
• In set allocation problems the monotonicity condition can be weakened.

We study ex post implementation in an interdependent value framework and with single dimensional types, using a class of mechanisms identified by monotonicity of outcomes and an integral representation of payments. We give examples to illustrate this class and its relation to the previous literature. The various extensions of the Vickrey–Clarke–Groves mechanism to interdependent value models are examples of this class. The extraction mechanisms of Crémer and McLean (1985) also form a special case for finite type spaces. The class is particularly useful in set allocation problems where the monotonicity condition is easier to work with.