Applied Math Colloquium | Robert McCann, Duality and free boundaries for optimal nonlinear pricing

Thursday, November 23, 2023 2:30 pm - 2:30 pm EST (GMT -05:00)

MC 5501 


Robert McCann, Department of Mathematics, University of Toronto 


Duality and free boundaries for optimal nonlinear pricing


The principal-agent problem is an important paradigm in economic theory for studying the value of private information;  the nonlinear pricing problem
faced by a monopolist is one example; others include optimal taxation and auction design. For multidimensional spaces of consumers (i.e. agents) and products, Rochet and Chon\'e (1998) reformulated this problem to a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a (quasi)linear sensitivity to prices. We characterize solutions to this problem by identifying a dual minimization problem.  This duality allows us to reduce the solution of the square example of Rochet-Chon\'e to a novel free boundary problem,  giving the first analytical description of an overlooked market segment.  

Based on work with KS Zhang (Fudan University) [81] at