Title: Hilbert Elasticity

Speaker: Zhigang Cao, Professor, Beijing Jiaotong University

Host: Zhuoran Lu, Associate Professor, Antai College of Economics and Management, Shanghai Jiao Tong University

Time: 14:00‑15:30, Thursday, September 24, 2026

Venue: Room A507, Antai College of Economics and Management, Xuhui Campus, Shanghai Jiao Tong University

Brief introduction of the content: 

By treating positive vectors as rays and using Hilbert's projective metric to measure their distance, we introduce the Hilbert elasticity, which generalizes the Hicks elasticity of substitution from two to arbitrary number of inputs, in a global way that is distinct from known ones.  Using oscillation semi-norm and Dobrushin coefficient, we provide simple characterization and closed-form formulas for computing the Hilbert elasticity. Applying the contraction mapping theory on the Hilbert metric, we find that the Hilbert elasticity is powerful in  proving up-to-scale uniqueness of fixed points, global convergence, and comparative statics. Using this framework, we obtain new results for the CES exchange economy in general equilibrium and gravity models in international trade. (joint with Sijie Wang)

Speaker's profile:

Zhigang Cao, Professor, School of Economics and Management, Beijing Jiaotong University. He graduated from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2010 and worked there as an Assistant Research Fellow. In September 2017, he joined the School of Economics and Management, Beijing Jiaotong University as a Professor under the “Excellent Hundred‑Talent Program”. His long‑term research covers cooperative games, transportation games, network games, and algorithmic game theory. He has published numerous papers in journals including Operations Research, Mathematics of Operations Research, Games and Economic Behavior, Journal of Mathematical Economics, Social Choice and Welfare, International Journal of Game Theory, and Science China‑Mathematics. His research achievements have earned him honors such as the Theoretical Contribution Award of China Information Economics, the Youth Science and Technology Award for Systems Science and Systems Engineering, the Youth Science and Technology Award for Chinese Decision Science, and the Guan Zhaozhi Young Research Award. He has presided over the Youth Project, General Project, and Excellent Young Scientist Project funded by the National Natural Science Foundation of China. He also serves as Vice‑Chairman of the Intelligent Decision and Game Theory Branch of China Society of “Two‑Methods” Research, Vice‑Chairman of the Game Theory Branch of the Operations Research Society of China, Deputy Secretary‑General of the Systems Engineering Society of China, Standing Director of the Chinese Information Economics Association, Director of the Society of Management Science and Engineering, and Director of the Operations Research Society of China.

Welcome all!