The course goal is to expose students to the research frontiers on matching markets from the context provided by the classic economics literature. Students will read and present recent current papers in the field as well as classic works from economics. The course first discusses basic ways to view one-to-one stable matching: as a lattice and as a polytope. We then investigate generalizations of this classic setting, discussing the one-to-many and many-to-many matchings and the constraints on preferences that make the standard matching algorithms valid in these extended settings. We then consider a different generalization, namely the assignment problem, in which only one side has preferences. Here we compare and contrast classic mechanisms. We conclude with a few recent results that investigate properties of matchings in large markets as well as applications of matching.
· Please attend the matching seminar on Feb. 18th and 19th (see http://www.kellogg.northwestern.edu/meds/matching2010/ for details).
· 18 January, 2011. “Job Matching, Coalition Formation, and Gross Substitutes” by Kelso and Crawford
· 27 January, 2011. “Matching with Contracts” by Hatfield and Milgrom
· 3 February, 2011. “Assignment Messages and the Assignment Exchange” by Milgrom
· 10 February, 2011. “The Geometry of Fractional Stable Matchings and Its Application” by Teo and Sethurama
· 17 February, 2011. “Stable Matching in a Common Generalization of the Marriage and Assignment Models” by Eriksson and Karlander
· 24 February, 2011. “Some Results on Stable Matchings and Fixed Points” by Fleiner, and “A New Fixed Point Approach for Stable Networks and Stable Marriages” by Feder
· 3 March, 2011. “On Cores and Indivisibility” by Shapley and Scarf , and “Re-allocation of Objects: Dealing with Indifference” by Jaramillo and Manjunath
· 10 March, 2011. “A Solution to the Random Assignment Problem” by Katta and Sethuraman, and “Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems” by Abdulkadiroglu and Sonmez
Axiomatic approaches (see “Efficient Resource Allocation on the Basis of Priorities” by Ergun), large market results (e.g., incentive properties of NRMP, existence of matchings with couples, strategyproofness of probabilistic serial mechanism), applications to specific markets (kidney exchange, school choice, NRMP).