This paper considers three challenge areas for mechanism design and describes the role approximation plays in resolving them. Challenge 1: optimal mechanisms are finely tuned to precise details of the distribution on agent preferences. Challenge 2: in environments with multi-dimensional agent preferences economic analysis has failed to provide general characterizations optimal mechanisms. Challenge 3: optimal mechanisms are parameterized by unrealistic knowledge of the distribution of agents' private preferences. This paper surveys positive resolutions to these challenges with emphasis on basic techniques and their relevance to theory and practice.

The optimal allocation of resources in complex environments—like allocation of dynamic wireless spectrum, cloud computing services, and Internet advertising—is computationally challenging even given the true preferences of the participants. In the theory and practice of optimization in complex environments, a wide variety of special and general purpose algorithms have been developed; these algorithms produce outcomes that are satisfactory but not generally optimal or incentive compatible. This paper develops a very simple approach for converting any, potentially non-optimal, algorithm for optimization given the true participant preferences, into a Bayesian incentive compatible mechanism that weakly improves social welfare and revenue.