A Unified Framework for Implementation, the Revelation Principle, and Optimal Approximation

Abstract

This paper attempts to provide a unified framework for implementation to capture both private information (hidden type) and private action (hidden action) aspects. (We generalize the Mount-Reiter triangle to a "square".) In addition, it takes a different approach to study mechanism design. Given a goal, rather than dealing with full and/or weakly implementation, we search an optimal mechanism in the sense that it best approximates the given goal among all the conceivable mechanisms. We extend privacy-preserving and the revelation principle to this more general setting. Based on the discussion of the properties of the space of incentive compatible mechanisms, the existence of an optimal incentive compatible mechanism is investigated. Stochastic mechanisms are also examined.