Finite supermodular design with interdependent valuations

- We study supermodular Bayesian mechanism design in quasi-linear environments with interdependent valuations and finite type spaces.
- Supermodular mechanisms induce the right incentives so that agents play a supermodular game.
- We show that any mechanism can be converted into a supermodular mechanism whose equilibrium set is of minimal size.
- We also present conditions for supermodular implementation in unique equilibrium.
- Certain social objectives cannot be reached with ex-post implementation yet they can with a supermodular mechanism with a unique equilibrium.

This paper studies supermodular mechanism design in environments with arbitrary (finite) type spaces and interdependent valuations. In these environments, the designer may have to use Bayesian equilibrium as a solution concept, because ex-post implementation may not be possible. We propose direct (Bayesian) mechanisms that are robust to certain forms of bounded rationality while controlling for equilibrium multiplicity. In quasi-linear environments with informational and allocative externalities, we show that any Bayesian mechanism that implements a social choice function can be converted into a supermodular mechanism that also implements the original decision rule. The proposed supermodular mechanism can be chosen in a way that minimizes the size of the equilibrium set, and we provide two sets of sufficient conditions to this effect. This is followed by conditions for supermodular implementation in unique equilibrium.