Econ 289 (Winter 2020)

Econ 289: Topics in Game Theory

Class Time: Mondays and Wednesdays, 1:30-3:20

Location: Landau, Room 206

Office Hours: by appointment

Instructor: Fuhito Kojima

fuhitokojima1979 “at” gmail.com

http://sites.google.com/site/fuhitokojimaeconomics/

(This syllabus is evolving: Please check the latest version frequently. Last updated: 12/09/2018)

How to match people to other people or goods is an important problem in society. Just think of some examples such as (1) student placement in schools, (2) labor markets where workers and firms are matched to one another, and (3) organ transplantation, in which patients are matched to potential donors. The economics of “matching and market design” has analyzed these problems and improved real-life institutions in recent years. For example, economists have helped (1) NYC, Boston and other U.S. cities design their school choice programs, (2) medical communities reorganize their hiring procedure, and (3) organize systematic kidney exchange mechanisms to give kidneys to as many patients as possible. This is a subject that attracted much attention in 2012, as the Nobel Prize in economics was awarded to Alvin Roth at Stanford and Lloyd Shapley at UCLA who are pioneers in matching and market design, and the John Bates Clark medal awarded to Parag Pathak in 2018.

This is a topics course. We discuss mechanism/market design, with the main (though not necessarily exclusive) focus on theory and application of matching theory. This class builds on material covered in Econ 285.

I will put emphasis on recent advances in the topic and present open questions so that interested students can promptly come to the frontier and begin their own research.

The first few weeks are delivered in the lecture style. Then the rest of the course is based on student presentations of recent research papers and possibly students' own ideas. We also have several guest lectures.

Grading

Grading will be based on class participation (discussion, student presentations) and a final paper (suggested length is 5-10 pages; it can be either your own research idea or you can write a critical literature review).

Prerequisite

Game theory at the 1st year PhD level. Also it is strongly recommended that you have taken Econ 285, because many of the topics are based on the material covered there. But Econ 285 is not a requirement. If you have not taken Econ 285, please familiarize yourself with the topic by taking a look at slides at, for example,

http://www.stanford.edu/~niederle/marketdesign2012.htm

Textbooks

The recommended textbook is

Two-Sided Matching by Roth and Sotomayor (1990) from Cambridge University Press.

I will also assign research papers.

Slides

Lectures 1 and 2

Guest lecture by Ning Neil Yu (1, 2)

Lecture 3

Lecture Topics (the plan is tentative and may evolve depending on student interests and how the class proceeds). Papers with * are the main readings for the class.

Class 1: Introduction/ Design of Labor Market Clearinghouses

• • *Roth and Sotomayor (1990), Chapters 2-4.

  • Gale, David and Lloyd Shapley (1962), “College Admissions and the Stability of Marriage” American Mathematical Monthly, 69, 9-15.

  • *Kojima, F. and Pathak, P. A. (2008), “Incentives and Stability in Large Two-Sided Matching Markets,” American Economic Review 99, pp 608-627.

  • *Alvin E. Roth and Elliott Peranson (1999) “The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design,” American Economic Review, 89 (4) September, 748-780

  • Kojima, F., Parag A. Pathak, and Alvin E. Roth (2013) "Matching with Couples: Stability and Incentives", Quarterly Journal of Economics.

  • Immorlica, N. and Mahdian, M. (2005), “Marriage, Honesty, and Stability,” SODA 2005, pp. 53–62.

  • SangMok Lee, (2014) Incentive Compatibility of Large Centralized Matching Markets [PDF]

  • Itai Ashlagi, Yash Kanoria, and Jacob Leshno (2013) Unblanaced Random Matching Markets: the Stark Effect of Competition, forthcoming, Journal of Political Economy

  • Itai Ashlagi, Mark Braverman, and Avinatan Hassidim, Stability in Large Matching Markets with Complementarities, forthcoming, Operations Research.

  • Yeon-Koo Che, Jinwoo Kim, and Fuhito Kojima, Stable Matching in Large Economies (2015), mimeo (R&R Econometrica)

Class 2: Matching with Distributional Constraints

· *Roth and Sotomayor (1990), Chapters 2 and 5.

Roth, A.E., "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, 92, 1984, 991-1016.

· *Roth (1986), On the allocation of residents to rural hospitals: a general property of two-sided matching markets, Econometrica

· *Yuichiro Kamada and Fuhito Kojima, Efficient Matching under Distributional Constraints: Theory and Applications, 2015, American Economic Review

Peter Biro, Tamas Fleiner, Robert Irving, and David Manlove, "The College Admissions Problem with Lower and Common Quotas", (2010), Theoretical Computer Sience.

· John William Hatfield and Fuhito Kojima, “Substitutes and Stability for Matching with Contracts” (2010), Journal of Economic Theory, 145, 1704-1723.

Goto, Hashimoto, Iwasaki, Kawasaki, Ueda, Yasuda, and Yokoo, "Strategy-Proof Matching with Regional Minimum Quotas" (2014) AAMA 2014.

Fragiadakis, Iwasaki, Troyan, Ueda, and Yokoo, Strategy-Proof Matching with Minimum Quotas (2015), forthcoming, ACM Transactions on Economics and Computation

Daniel Fragiadakis and Peter Troyan, Market Design under Distributional Constraints: Diversity in School Choice and Other Applications (2015), forthcoming, Theoretical Economics

Yuichiro Kamada and Fuhito Kojima, "Stability Concepts in Matching under Distributional Constraints ", mimeo

Yuichiro Kamada and Fuhito Kojima, General Theory of Matching under Distributional Constraints (2015), mimeo

Fuhito Kojima, Akihisa Tamura, and Makoto Yokoo, Designing Matching Mechanisms under Constraints: An Approach from Discrete Convex Analysis, (2015), mimeo

Class 3: Design of Random Assignment Mechanisms (1)

• • Abdulkadiroglu, A., and T. Sonmez (2003) “Ordinal Efficiency and Dominated Sets of Assignments,” Journal of Economic Theory, 112, 157—172.

• Abdulkadiroglu, A., and T. Sonmez (1998): “Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems,” Econometrica, 66, 689-698.

• *Bogomolnaia, A., and H. Moulin (2001), “A New Solution to the Random Assignment Problem,” Journal of Economic Theory, 100, 295-328.

• *Che, Yeon-Koo and Fuhito Kojima, “Asymptotic Equivalence of Random Priority and Probabilistic Serial Mechanisms,” forthcoming, Econometrica.

• Hylland and Zeckhauser (1979), “The efficient allocation of Individuals to Positions”, Journal of Political Economy.

• Katta, A.-K. and J. Sethuraman, “A solution to the random assignment problem on the full preference domain” (2006), Journal of Economic Theory.

• Kesten, O, “Why Do Popular Mechanisms Lack Efficiency in Random Environments?,” forthcoming, journal of economic theory.

• *Fuhito Kojima and Mihai Manea, “Incentives in the Probabilistic Serial Mechanism,” forthcoming, Journal of Economic Theory.

• Fuhito Kojima, “Random Assignment of Multiple Indivisible Objects” (2007), forthcoming, Mathematical Social Sciences.

• McLennan A., “Ordinal efficiency and the polyhedral seperating hyperplane theorem,” Journal of Economic Theory 105 (2002), 435-449.

• Yilmaz, O., “House Allocation with Existing Tenants: A New Solution,” mimeo

• Manea, Mihai, “Asymptotic Ordinal Inefficiency of Random Serial Dictatorship,” forthcoming, Theoretical Economics.

Class 4: Design of Random Assignment Mechanisms (2):

• • Hylland and Zeckhauser (1979), “The efficient allocation of Individuals to Positions”, Journal of Political Economy.

  • *Eric Budish, Yeon-Koo Che, Fuito Kojima, and Paul Milgrom (2013), “Designing Random Allocation Mechanisms: Theory and Applications”, American Economic Review

  • Tadashi Hashimoto, Daisuke Hirata, Onur Kesten, Morimitsu Kurino, and M. Utku Unver, Two Axiomatic Approaches to the Probabilistic Serial Mechanism. Theoretical Economics

  • Mohammad Akbarpour and Afshin Nikzad, Approximate Random Allocation Mechanisms, mimeo

Classes 5-: Student Presentations

I have assigned papers to each date of class after the first few lectures by me. There are TBA slots. Each student should sign up for TBA dates (subject to change depending on enrollment). I will send a google docs link to class by the end of the firsts week so that everyone enrolled can sign up for slots.

Below are reading lists from previous years. In the past I taught from subsets from these topics. I keep them here iin case you are interested, although I will not cover them this year.

Resource allocation with multi-unit demands

*Eric Budish, The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes

*Eric Budish and Estelle Cantillon, The Multi-Unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard

Eric Budish, Yeon-Koo Che, Fuhito Kojima, and Paul Milgrom, Implementing Random Assignments: A Generalization of the Birkhoff-von Neumann Theorem (2009),

Kojima, F, Random Assignment of Multiple Indivisible Objects (2007), forthcoming, Mathematical Social Sciences.

Fuhito Kojima, Efficient Resource Allocation under Multi-unit Demand (2013), Games and Economic Behavior

John William Hatfield, Strategy-proof, efficient, and nonbossy quota allocations, Social Choice and Welfare, 2009.

Mihai Manea, Serial dictatorship and Pareto optimality, Games and Economic Behavior, 2007.

Aanund Hylland and Richard Zeckhauser, The efficient allocation of individuals to positions, JPE 1979.