This course surveys a number of economic topics of current research interest in which mathematical developments have (and are expected to continue to) contribute crucial advances. These include the theory of matching and pricing, problems of asymmetric information, the principle-agent framework, auction theory, mechanism (and information) design, portfolio optimization and hedging. These topics are unified through a linear program approach in which the mathematical theory of optimal transport and its emerging relevance figure prominently.

References:

Basov. Multidimensional Screening. Springer, 2005.

Chiappori. Matching with Transfers: The Economics of Love and Marriage. Princeton, 2017.

Galichon. Optimal Transport Methods in Economics. Princeton, 2016.

Henry-Labord\`ere. Model-free Hedging: A Martingale Optimal Transport Viewpoint. CRC Press 2017.

Mas-Colell, Whinston and Green. Microeconomic Theory. Oxford, 1995.

Sotomayor and Roth. Two-Sided Matching: a Study in Game-Theoretic Modeling and Analysis. Cambridge Press, 1992.

Santambrogio. Optimal Transport for Applied Mathematicians. Birkhauser 2015.

Vohra. Mechanism Design: A Linear Programming Approach. Cambridge 2011.