Abstract:
We consider a robust mechanism design problem in which a seller wishes to choose a selling mechanism to maximize the revenue obtained from a buyer with private willingness-to-pay information and a nonlinear utility function. The objective is to provide a profit guarantee for the seller across all possible willingness-to-pay distributions whose mean and variance are consistent with the prior information. When the utility function is of a quadratic form and the coefficient of variation is low, we find that a quadratic pricing mechanism yields the optimal revenue guarantee. In this case, the worst-case distribution of willingness-to-pay follows a Pareto distribution. However, when the coefficient of variation is high, a unit price mechanism is optimal. We further extend our analysis to general elasticity utility functions and investigate how the optimal worst-case revenue varies with elasticity and coefficient of variation. Furthermore, given the widespread implementation of a two-part tariff mechanism in real-world scenarios, we also study the optimal two-part tariff mechanism. We show that under the quadratic utility form, the optimal two-part tariff pricing strategy achieves at least 80% of the optimal worst-case revenue when compared with the optimal robust mechanism. We also develop corresponding performance guarantees when the elasticity coefficient is less than two. However, when the elasticity coefficient exceeds two, the competitive ratio of the two-part pricing scheme goes to zero as the variance of willingness-to-pay grows to infinity.
About the speaker:
Prof. Zizhuo Wang is a Professor and Associate Dean at the School of Data Science. He is also the co-founder and CTO of Cardinal Operations (杉数科技). He obtained his bachelor's degree in Mathematics from Tsinghua University in 2007, and his Ph.D. degree in Operations Research from Stanford University in 2012. Prior to joining CUHK-Shenzhen, he was an Associate Professor (with tenure) in the Department of Industrial and Systems Engineering at the University of Minnesota.
His research interests mainly focus on optimization and stochastic modeling, especially with applications to pricing and revenue management. He has published over 50 papers in top journal in the field of operations research and management science, and has been the Associate Editors or Senior Editors for the top journals such as Management Science, Operations Research, MSOM and POMS. His research has been supported by the National Natural Science Foundation of China (NSFC), the National Science Foundation (NSF) in the United States and other funding agencies, with a total amount of near 10M RMB.
Zizhuo Wang has extensive experiences in applying data-driven methods in industry. In 2016, he co-founded Cardinal Operations with others, which served over 200 enterprises to provide data-driven decision support service and products.