Approximation in mechanism design

This talk surveys three challenge areas for mechanism design and describes the role approximation plays in resolving them. Challenge 1: optimal mechanisms are parameterized by knowledge of the distribution of agent's private types. Challenge 2: optimal mechanisms require precise distributional information. Challenge 3: in multi-dimensional settings economic analysis has failed to characterize optimal mechanisms. The theory of approximation is well suited to address these challenges. While the optimal mechanism may be parameterized by the distribution of agent's private types, there may be a single mechanism that approximates the optimal mechanism for any distribution. While the optimal mechanism may require precise distributional assumptions, there may be approximately optimal mechanism that depends only on natural characteristics of the distribution. While the multi-dimensional optimal mechanism may resist precise economic characterization, there may be simple description of approximately optimal mechanisms. Finally, these approximately optimal mechanisms, because of their simplicity and tractability, may be much more likely to arise in practice, thus making the theory of approximately optimal mechanism more descriptive than that of (precisely) optimal mechanisms. The talk will cover positive resolutions to these challenges with emphasis on basic techniques, relevance to practice, and future research directions.