'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

Applications are not open yet. Seats will be limited. To apply, a from will be available to fill out and applicants should have a faculty advisor send a reference letter to math.econ.code@gmail.com. The deadline to apply will be May 1, 2022.
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
Parallel computing
Principles of parallelization; computing on the cloud; use of the numba library.
July
SPECIAL
lecture 2
Special matrices
Z, P and Mmatrices, diagonally dominant matrices, Stieltjes matrices, and PerronFroebenius theory. Mmaps and inverse isotonicy.
September
SPECIAL
lecture 3
Submodularity
Lattices, submodularity and Topkis’ theorem. Veinott's order. Monotone comparative statics. Strategic complementarities.
October
SPECIAL
lecture 4
Gross substitutes
Polymatroids, exchangeability.
Lovasz extensions.
Discrete convex analysis, L / L# / M / M# convexity. Unified Gross Substitutes.
November
SPECIAL
lecture 5
Matching with contracts
Kelso and Crawford’s deferred acceptance algorithm. Hatfield and Milgrom’s model of matching with contracts.
December