Growing evidence suggests that breaking dominant strategy incentive compatibility in favor of increasing a mechanism's transparency---i.e., allowing agents to observe more about others' past moves---may sometimes achieve closer conformity to the designer's objective. To help increase the practical efficacy of mechanism design, in this paper we provide a theoretical framework to predict in advance when this is the case.

We propose a measure of strategic complexity for strategy-proof mechanisms. In particular, we characterize a class of implementations for which we provide a complete ranking in terms of their strategic complexity, in a well-defined sense. The class---which we call essential frames---includes virtually all strategy-proof mechanisms used in practice.