MAT 1855H Homepage: Mathematical Problems in Economics

Professor Robert McCann

FUTURE MEETINGS:
16h10 - 17h40 Tuesdays and Thursdays BA 6183
OFFICE HOURS:
immediately following each class in BA 6124

Course information

POSSIBLE TOPICS

Gale & Shapley (1962) The College Admissions Problem (NTU Matching by Deferred Acceptance); see also books by Knuth '81 and Roth and Sotomayor '90
McCann & Guillen `Five Lectures' (2013)
Shapley & Shubik (1972) The Assignment Game I (TU Matching is a linear program)
Rigorous approaches to duality
Principal Agent Problems with Multidimensional Heterogeneity
Rochet & Chone (1998) Ironing, Screening and Multidimensional Sweeping
Armbruster (2013+) A short proof of Strassen's theorem using convex analysis
C{1,1} Regularity for principal-agent problems , with Cale Rankin and Kelvin Shuangjian Zhang. arXiv 2303.04937
Remark on Rochet and Chone's square screening example, with Kelvin Shuangjian Zhang. To appear in J. Convex Anal., arXiv 2311.13012
A duality and free boundary approach to adverse selection, with Kelvin Shuangjian Zhang. To appear in Math. Models Methods Appl. Sci., arXiv 2301.07660
Figalli, Kim & McCann (2011) When is multidimensional screening a convex program?
McCann & Zhang (2019) On concavity of the monopolist's problem facing consumers with nonlinear price preferences
Noldeke & Samuelson (2018) The Implementation Duality

Myerson (1981) Optimal Auction Design
Kinderlehrer and Nirenberg(1977) Regularity in free boundary problems
Figalli (2018+) Free boundary regularity in obstacle problems

PROJECT SUGGESTIONS

Akerlof (2001) Behavioral Macroeconomics and Macroeconomic Behavior
Choo & Siow (2006) Who marries whom and why
Hotelling (1929) Stability in competition (why duopoly may fail to produce variety)
Kuhn (1955) Hungarian Algorithm (also integrality and alternate approach to duality) and Historical Restrospective (2012)
Mirrlees (1996) Information and Incentives: The Economics of Carrots and Sticks
Shimer and Smith (2000) Matching with Search Costs
Sonnenschein (1982) Myopic price dynamics (the first example of a Wasserstein gradient flow)
Stiglitz (2001) Information and the Change in Paradigm in Economics
Laffont (1996) William Vickrey: A Pioneer in the Economics of Incentives
Wong (2016) Geometry and Optimization of Relative Arbitrage