Finite supermodular design with interdependent valuations

Abstract

This paper studies supermodular mechanism design in environments with finite type spaces and interdependent valuations. In such environments, it is difficult to implement social choice functions in ex-post equilibrium, hence Bayesian Nash equilibrium becomes the appropriate equilibrium concept. The requirements for agents to play a Bayesian equilibrium are strong, so we propose mechanisms that are robust to bounded rationality and help guide agents towards an equilibrium. In quasi-linear environments that allow for informational and allocative externalities we show that any mechanism that implements a social choice function can be converted into a supermodular mechanism that implements the original social choice function's decision rule. We show that the supermodular mechanism can be chosen in a way that minimizes the size of the equilibrium set and provide two sets of sufficient conditions: for general decision rules and for decision rules that satisfy a certain requirement. This is followed by conditions for supermodular implementation with a unique equilibrium.

Full Implementation and Belief Restrictions

“…Deb and Pai (2017), for instance, pursue symmetry of the mechanism. Mathevet (2010) and Mathevet and Taneva (2013) instead pursue supermodularity. In those papers, the extra desiderata are achieved by adding a belief-dependent component to some baseline payments, much as we attain full implementation appending an extra term to the canonical transfers.…”