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This page collects my work on the market design problem of course allocation, also known as multi-unit or combinatorial assignment. My best known conceptual ideas in this area are the course allocation mechanism “Approximate Competitive Equilibrium from Equal Incomes” (A-CEEI) and the associated approximate fairness and incentives criteria: Envy Bounded by a Single Good (EF-1), Maximin Share (MMS), and Strategy-proof in the Large (SP-L).

Confusingly, my papers developing A-CEEI were published in reverse chronological order (our profession’s beautiful publication process). I recommend reading the early papers in the order Budish and Cantillon (2012), then Budish (2011), then Othman et al (2010).

A good summary of my overall methodological approach is in the essay “Matching ‘versus’ Mechanism Design.”

The A-CEEI mechanism is now used in practice for course allocation at several leading universities. The company behind this is Cognomos. The research that helped bring A-CEEI from theory to practice is the 2017 Operations Research paper and the 2021 Management Science paper.

Selected Materials

Research Papers

Practical Algorithms and Experimentally Validated Incentives for Equilibrium-based Fair Division (A-CEEI)

Coauthors: Ruiquan Gao, Abraham Othman, Aviad Rubinstein, and Qianfan Zhang
EC '23: Proceedings of the 24th ACM Conference on Economics and Computation, (2023): 337-368.
Al Roth’s Market Design Blog
[PDF] [All Related Material]

Can Market Participants Report their Preferences Accurately (Enough)?

Coauthors: Judd B Kessler
Management Science, (2022): 68, no. 2, 1107–1130.
[PDF] [Slides] [All Related Material]

An Improved Bound for the Shapley-Folkman Theorem

Coauthors: Philip J Reny
Journal of Mathematical Economics, (2020): 89, 48-52.
[PDF] [All Related Material]

Course Match: A Large-Scale Implementation of Approximate Competitive Equilibrium from Equal Incomes for Combinatorial Allocation

Coauthors: Gerard Cachon, Judd B Kessler, Abraham Othman
Operations Research, (2017): 65, no. 2, 314-336.
Wharton “Course Match” website
Cognomos
The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes
[PDF] [Slides] [All Related Material]

Designing Random Allocation Mechanisms: Theory and Applications

Coauthors: Yeon-Koo Che, Fuhito Kojima, and Paul Milgrom
American Economic Review, (2013): 103, no. 2, 585-623.
[PDF] [Slides] [All Related Material]

Matching “Versus” Mechanism Design

ACM SIGecom Exchanges, (2012): 11, no. 2, 4-15.
[PDF] [Slides] [All Related Material]

The Multi-Unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard

Coauthors: Estelle Cantillon
American Economic Review, (2012): 102, no. 5, 2237-2271.
Slides, Jerusalem Summer School (Summer 2014)
Slides, Columbia Seminar (Nov 2009)
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The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes

Journal of Political Economy, (2011): 119, no. 6, 1061-1103.
Wikipedia entry: Course allocation
Wikipedia entry: Maximin share
Wharton “Course Match” website
Cognomos
Slides, Jerusalem Summer School (Summer 2014)
Job Market Talk Slides (Feb 2009)
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Finding Approximate Competitive Equilibria: Efficient and Fair Course Allocation

Coauthors: Abraham Othman and Tuomas Sandholm
Proc. of 9th Int. Conf. on Autonomous Agents and Multiagent Systems (AAMAS 2010), (2010): 1, 873-880.
[PDF] [All Related Material]