ALFRED GALICHON'S
MASTERCLASSES
'math+econ+code' masterclass
on equilibrium transport
and matching models in economics
June 1317, 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, PerronFroebenius 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 firstyear 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 1317, 2022, 8am  12noon US Eastern time / 2pm6pm 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
Distancetofrontier function, matching function equilibrium. Matching models with taxes. Collective models with public consumption.
Day 4: matching models with nontransferable 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 BellmanFord’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
46pm Paris time/
10amnoon NY time
Special matrices

Z, P and Mmatrices

diagonally dominant matrices

Stieltjes matrices, and PerronFroebenius theory

Mmaps and inverse isotonicy
SPECIAL
lecture 2
Submodularity
September 30 2022
46pm Paris time/
10amnoon NY time

Lattices

Submodularity and Topkis’ theorem

Veinott's order

Monotone comparative statics

Strategic complementarities
SPECIAL
lecture 3
Parallel computing
October 28 2022
46pm Paris time/
10amnoon NY time
Guest lecture: Flavien Léger

Principles of parallelization

Computing on the cloud

Use of the numba library
SPECIAL
lecture 4
Gross substitutes
November 18 2022
46pm Paris time/
10amnoon NY time

Polymatroids, exchangeability

Lovasz extensions

Discrete convex analysis

L / L# / M / M# convexity

Unified Gross Substitutes
SPECIAL
lecture 5
Matching with contracts
December 16 2022
46pm Paris time/
10amnoon NY time

Kelso and Crawford’s deferred acceptance algorithm

Hatfield and Milgrom’s model of matching with contracts