Research Projects

Multi-dimensional auctions are widely used in e-commerce, with applications such as sponsored search auctions for search engines, spectrum auctions for governments, and sellers selling heterogeneous items to buyers. The revenue-maximizing auction mechanism in multi-item settings has been discovered for certain valuations but remains unknown for other distributions. This project aims to identify a unified approach to compute the revenue-optimal mechanism in the two-buyer one-item setting, solve the problem in the multiple-buyer setting for some simple distributions, and extend results to the dynamic setting. The research will focus on three main problems: computing the revenue-optimal auction mechanism in the two-item one-buyer setting, determining the right mathematical model for the multi-buyer setting, and designing the revenue-optimal solution for simple distributions. In the two-item one-buyer dynamic setting, the optimization problem will be formulated using EPIR constraint and techniques based on dynamic programming. The results from designing the revenue-optimal mechanism in multi-dimensional static settings will assist in solving the problem in dynamic settings. In conclusion, this project aims to identify a unified approach to computing the revenue-optimal mechanism in various e-commerce settings, including the two-item one-item setting, multiple-buyer setting, and dynamic setting.