ALFRED GALICHON'S
MASTERCLASSES
'math+econ+code' masterclass
on equilibrium transport
and matching models in economics
June 13-17, 2022
This intensive course, part of the 'math+econ+code' series, is focused on the computation of competitive equilibrium with substitutes, which is at the core of surge pricing engines and allocation mechanisms. It will investigate diverse applications such as surge pricing, matching platforms and network congestion. It provides a bridge between theory, empirics and computation and will introduce tools from economics, mathematical and computer science. Students will have the opportunity to write their own code (in Python), in the spirit of cooking lessons. Mathematical concepts (such as lattice programming, supermodularity, discrete convexity, Perron-Froebenius theory, etc.) will be taught on a needs basis while studying various economic models. The same is true of computational methods (such as tatonnement algorithms, asynchronous parallel computation, mathematical programming under equilibrium constraints, etc.). Hence there are no prerequisite other than the equivalent of a first-year graduate sequence in econ, applied mathematics or other quantitative disciplines.
This course is very demanding from students, but the learning rewards are high.
Practical information
• The course will be taught online over five consecutive days, June 13-17, 2022, 8am - 12noon US Eastern time / 2pm-6pm Paris time.
• Additionally, five advanced lectures will be taught online on a monthly basis afterwards, July -December 2022. Precise days of the lectures will be announced later.
Applications are now closed
Course outline
Day 1: competitive equilibrium
with gross substitutes
Monday, 4h
Walrasian equilibrium and gross substitutes. Hedonic pricing. Jacobi algorithm.
Day 2: matching models with transferable utility
Tuesday, 4h
Optimization and equilibrium formulation. Duality. Computation by descent methods. Sinkhorn's algorithm.
Day 3: matching models with imperfectly transferable utility
Wednesday, 4h
Distance-to-frontier function, matching function equilibrium. Matching models with taxes. Collective models with public consumption.
Day 4: matching models with non-transferable utility
Thursday, 4h
Gale and Shapley’s deferred acceptance algorithm. Adachi’s algorithm and Tarski's fixed point theorem. Aggregate stable matchings.
Day 5: equilibrium on networks
Friday, 4h
Equilibrium pricing on networks. Scheduling, dynamic programming and Bellman-Ford’s algorithm.
+ 5 advanced lectures
July to November, 2h each
Lectures on related advanced mathematical / computational topics to complement the masterclasses and solidify the theoretical knowledge.
Advanced lectures
SPECIAL
lecture 1
August 26 2022
4-6pm Paris time/
10am-noon NY time
Special matrices
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Z-, P- and M-matrices
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diagonally dominant matrices
-
Stieltjes matrices, and Perron-Froebenius theory
-
M-maps and inverse isotonicy
SPECIAL
lecture 2
Submodularity
September 30 2022
4-6pm Paris time/
10am-noon NY time
-
Lattices
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Submodularity and Topkis’ theorem
-
Veinott's order
-
Monotone comparative statics
-
Strategic complementarities
SPECIAL
lecture 3
Parallel computing
October 28 2022
4-6pm Paris time/
10am-noon NY time
Guest lecture: Flavien Léger
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Principles of parallelization
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Computing on the cloud
-
Use of the numba library
SPECIAL
lecture 4
Gross substitutes
November 18 2022
4-6pm Paris time/
10am-noon NY time
-
Polymatroids, exchangeability
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Lovasz extensions
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Discrete convex analysis
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L / L# / M / M# convexity
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Unified Gross Substitutes
SPECIAL
lecture 5
Matching with contracts
December 16 2022
4-6pm Paris time/
10am-noon NY time
-
Kelso and Crawford’s deferred acceptance algorithm
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Hatfield and Milgrom’s model of matching with contracts