MAT 1855HS Homepage: Mathematical Problems in Economics



Professor Robert McCann

FUTURE MEETINGS:
14h10 - 15h40 Tuesdays and Thursdays FI 210
OFFICE HOURS:
16h45 - 17h30 Thursdays BA 6124

Course information


PAST LECTURES CAN BE VIEWED HERE

SOURCES

Jan 8 Gale & Shapley (1962) The College Admissions Problem (NTU Matching by Deferred Acceptance); see also books by Knuth '81 and Roth and Sotomayor '90
Jan 10 McCann & Guillen `Five Lectures' (2013)
Jan 17 Shapley & Shubik (1972) The Assignment Game I (TU Matching is a linear program)
Jan 21 Rigorous approaches to duality
Brezis (2018) Afriat (1963) | Gangbo & McCann (1995) | Gangbo & McCann (1996) | Kuhn (1955) | Santambrogio's Book 1.6.3

FUTURE
Rochet & Chone (1998) Ironing, Screening and Multidimensional Sweeping
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
Daskalakis, Deckelbaum & Tzamos (20017) Strong Duality For a Multiple Good Monopolist

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


RANDOM LINKS (to be edited)

Kantorovich (1942) and Koopmans (1949)
Rockafellar (1966)
Brenier (1987)
Caffarelli (1996)
Aleksandrov (1942a)
McCann (1995)
Lorentz (1953) | McCann (1999, Appendix A)


Evans Survey (1999)
Santambrogio "Optimal Transport for Applied Mathematicians" Birkhauser (2015)
Villani "Topics in Optimal Transportation" AMS (2003)
Villani "Optimal transport: old and new"


McCann (2014)