The Quantitative View of Myerson Regularity

In mechanism design, Myerson regularity is often too weak for a quantitative analysis of performance. For instance, ratios between revenue and welfare, or sales probabilities may vanish at the boundary of Myerson regularity. This paper therefore explores the quantitative version of Myerson regularity, which we call λ-regularity. It measures how Myerson regular a distribution is. In doing so, we unify separate literatures in economics, computer science, applied mathematics and statistics. The concept has appeared before, e.g., under the names of ρ-concavity and α-strong-regularity. We provide many new results for quantitative auction and mechanism design.