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

MC 5501 

Speaker

Robert McCann, Department of Mathematics, University of Toronto 

Title

Duality and free boundaries for optimal nonlinear pricing

Abstract

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 http://www.math.toronto.edu/mccann/publications