Two courses on matching and market design in Stanford's MS&E department, by Ashlagi and Saberi (first meeting is today)

Itai Ashlagi and  Amin Saberi are offering courses on matching theory and market design this quarter. First meetings are today, in the morning and in the afternoon:

MS&E 230: Market design for engineers

Itai Ashlagi  T-Thu 9:45-11:15

Course description:  Marketplaces use algorithms and sets of rules in order to allocate resources among self-interested agents, who often hold necessary information. This course will provide key principles in engineering a marketplace, to identify relation between the rules in the marketplace and market failures, and how to redesign them to achieve desirable outcomes.  The course provides foundations of resource allocation systems building on game theoretic analysis.  The course explores economic and algorithmic tools from matching, mechanism design, auction theory and information design. Cases of existing and future marketplaces will be discussed, including ride-sharing systems, school choice programs, online dating, online advertising and organ allocation.

Some applied questions include: How should we assign students to schools? How should we match doctors to residency programs? Shall we price roads and the impact of tolls? How should we allocate affordable housing and arrange waiting lists? How should we incentivize hospitals to collaborate on kidney exchanges? How should we allocate food to food banks? How should reduce organ discards?  How can we assist in migration?  Why is some marketplace decentralized (college admissions) and others are more controlled? How should platforms set incentives? What incentives and frictions arise in blockchains? 

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MS&E 319: Matching Theory
Amin Saberi  T Th 01:30p-03:00p

The theory of matching with its roots in the work of mathematical giants like Euler and Kirchhoff has played a central and catalytic role in combinatorial optimization for decades. More recently, the growth of online marketplaces for allocating advertisements, rides, or other goods and services has led to new interest and progress in this area.  

The course starts with classic results characterizing matchings in bipartite and general graphs and explores connections with algebraic graph theory and discrete probability. Those results are complemented with models and algorithms developed for modern applications in market design, online advertising, and ride-sharing.

Topics include: 

Matching, determinant, and Pfaffian
Matching and polynomial identity testing
Isolating lemma and matrix inversion, matching in RNC

Combinatorial and polyhedral characterizations 
The assignment problem and its dual, primal-dual, and auction algorithms
Tutte’s theorem, Edmond’s LP, and the Blossom algorithm

The Gallai-Edmonds decomposition, Berge-Tutte formula, and applications in Nash bargaining

The stable marriage problem
Gale-Shapley theorem, incentive and fairness issues
LP characterization, counting stable matchings

Matching in dynamic environments
Online matching under various arrival models
Applications in ride-sharing and online advertising

 

Computation of matching  

Combinatorial vs continuous algorithms, near-linear time algorithms

Matchings in sub-linear time, streaming computational models

Sparsifiers and stochastic matching 

Counting matchings  
The Van der Waerden conjecture, Bregman-Minc’s inequality
Deterministic approximations, counting matchings in planar graphs
Markov chain Monte Carlo algorithms, sequential importance sampling
The Ising model, applications, and basic properties

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