Matching Theory | マッチング理論
Special Lectures in Economics | 経済学特論
Syllabus in English | 講義シラバス（日本語）
1st semester, Thursdays 2nd, Room 32
Office Hours: Wednesdays 9:50 - 10:50
Last update | 最終更新日: July 18, 2014
Announcement | お知らせ
A final report must be submitted by July 31. Please send your file via e-mail! 2014/7/18 New!
There will be NO lecture on May 1. 2014/4/24
The materials (two papers) for the second lecture are available in front of my office (Room 338). 2014/4/15
If you plan to attend this course (even if you are just sitting), please fill THIS FORM on-line as soon as possible! 2014/4/10
Lectures will be given in English, while your questions/comments as well as presentations can be Japanese. 2014/4/10
The first lecture will be on April 10th (Thu). 2014/3/17
Course Objective and Content | 講義概要・目的
We study the theory of two-sided matching. First, lectures based on the textbook are given. Then, we read recent academic papers on this subject.
The below is a tentative plan of the course. Lectures cover only 1 and 2. We study 3 and 4 through your presentations.
Basic models of two-sided matching
Monotone approach
Introduction of wages and contracts
Matching market design
Grading Policy | 成績評価
Based on the presentation and final report.
Auditing students SHOULD also make presentation but need NOT submit the final report.
Presentation can be given in Japanese or English, but SLIDES (you are encouraged to use them) must be typed in ENGLISH. I plan to invite your presentation in the lectures that are colored blue on course schedule below.
Final report can be written in Japanese or English. Your report should be either 1) original paper/idea on matching theory or 2) referee report on a paper on matching market design (which is not directly covered in class). Suggested length is 3 - 6 pages.
Textbooks | 講義テキスト
Main Textbook: Roth and Sotomayor, Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis, 1990. Amazon (Kindle)
The "bible" of matching theory, which contains almost all results in the literature up to 80s.
Reference 1: Gusfield and Irving, The Stable Marriage Problem: Structure and Algorithms, 1989. Amazon
Traditional matching theory from the viewpoint of computer science or operations research.
Reference 2: Vulkan, Roth, and Neeman ed., Handbook of Market Design, 2013. Amazon TOC
This book is so expensive that I won't encourage you to purchase. Relevant chapters might be distributed in class.
You are expected to read all double-starred (**) articles and encouraged to read starred(*) articles below.
Lectures on Matching Market Design | マッチング・マーケットデザイン講義
Tayfun Sonmez | Boston College
Itay P. Fainmesser | Brown U.
Alvin E. Roth | Harvard U.
Parag Pathak | MIT
Nicole Immorlica | Northwestern U.
Fuhito Kojima | Stanford U.
Muriel Niederle | Stanford U.
Scott Duke Kominers | U. of Chicago
Lecture 1 Introduction 4/10
Frontier of Economics
Market Design in Practice
"Matching" Problem and its Solution
"Exchange" Problem and its Solution
References
*Roth and Sotomayor: Ch1
*Roth, A. (2002)
*Roth, A. (2008a)
Economic Sciences Prize Committee of the Royal Swedish Academy of Sciences (2012)
Kojima, F. and Troyan, P. (2011)
Niederle, M., Roth, A. and Sonmez, T. (2008)
Lecture 2 One-to-One Matching Model 4/17
Two-Sided Market
Stable Matching
Gale-Shapley "Deferred Acceptance" Algorithm
M(W)-Optimal Matching
Lattice: Examples
References
**Roth and Sotomayor: Ch2
**Gale, D. and Shapley, L. (1962)
*Roth, A. (2008b)
Abdulkadiroglu, A. and Sonmez, T. (2013) Amazon
Knuth, D. (1976) Amazon
Sotomayor, M. (1996)
Lecture 3 Mathematical Structures of Stable Matchings 4/24
Lattice: Mathematical Structure
Decomposition Lemma
Weak Pareto Optimality
Path to Stable Matching
References
**Roth and Sotomayor: Ch2
*Gale, D and Sotomayor, M. (1985a)
Blair, C. (1988)
Demange, G., Gale, D and Sotomayor, M. (1987)
Gusfield and Irving (1989)
Roth, A. and Vande Vate, J. (1990)
Lecture 4 Incentive Issues 5/8
Core
Blocking Lemma
Strategy Proof-ness
Impossibility/Possibility Theorem
Equilibrium Behavior
References
**Roth and Sotomayor: Ch3; Ch4
*Gale, D and Sotomayor, M. (1985b)
*Roth, A. (1982)
Alcalde, J. and Barbera, S. (1994)
Dubins, L. and Freedman, D. (1981)
Roth, A. and Rothblum, U. (1999)
Lecture 5 Monotone Method 5/15
Partial Order
Lattice and Sublattice
Tarski's Fixed Point Theorem
Pre-Matching
References
**Adachi, H. (2000)
*Vives, X. (1999): Ch2 Amazon
Echenique, F. (2005)
Echenique, F. and Oviedo, J. (2004)
Milgrom, P. and Roberts, J. (1990)
Milgrom, P. and Roberts, J. (1994)
Tarski, A. (1955)
Lecture 6 One-to-Many Matching Model 5/22
College Admissions Model
Responsive Preferences
Strict Core
Rural Hospitals Theorem
References
**Roth and Sotomayor: Ch5
*Sotomayor, M. (1999)
Roth, A. (1984b)
Roth, A. (1985)
Roth, A. (1986)
Roth, A. and Sotomayor, M. (1989)
Presentation 1 Summary of William Thomson's Lectures (web) 5/29
Claims Problems --- Zhou Yu slide
Single-Peaked Preferences --- Puchit Sariddichainunta slide
Lecture 7 Matching with Money 6/5
Substitutable Preferences
Labor Market with Salaries
Gross Substitutes Condition
Salary-Adjustment Process
Budget Constraints
References
**Roth and Sotomayor: Ch6
*Kelso, A. and Crawford, V. (1982)
*Shapley, L. and Shubik, M. (1971)
Crawford, V. and Knoer, E. (1981)
Demange, G. and Gale, D. (1985)
Mongell, S. and Roth, A. (1986)
Lecture 8 One-Sided Matching Model 6/12
House Allocation Problem
Serial Dictatorship
Housing Market
Top Trading Cycles
YRMH-IGYT
Kidney Exchange Problem
References
**Sonmez, T. and Unver, U. (2011)
*Roth, A. and Postlewaite, A. (1977)
*Shapley, L. and Scarf, H. (1974)
Abdulkadiroglu, A. and Sonmez, T. (1999)
Bogomolnaia, A. and Moulin, H. (2001)
Hylland, A. and Zeckhauser, R. (1977)
Ma, J. (1994)
Quinzii, M. (1984)
Sonmez, T. and Unver, U. (2005)
Presentation 2 Applications (1) - Medical Residency Matching 6/19
Ch5 of Roth and Sotomayor --- Kohei Shiozawa
Roth, A. and Peranson, E. (1999) --- Hikaru Kondo
References
**Roth, A. (1984a)
**Roth, A. and Peranson, E. (1999)
*Roth and Sotomayor: Ch1; Ch5
Bulow, J. and Levin, J. (2006)
Kojima, F. and Pathak, P. (2009)
Kojima, F., Pathak, P., and Roth, A. (2013)
Mongell, S. and Roth, A. (1991)
Niederle, M. and Roth, A. (2003a)
Roth, A. (1991)
Roth, A. (2003)
Presentation 3 Applications (2) - Public School Choice 6/26
Abdulkadiroglu, A. and Sonmez, T. (2003) --- Koichi Fukumura
Balinski M and Sonmez, T. (1999) --- Shota Watabe
References
**Abdulkadiroglu, A. and Sonmez, T. (2013)
*Abdulkadiroglu, A. and Sonmez, T. (2003)
*Balinski M and Sonmez, T. (1999)
Abdulkadiroglu, A., Pathak, P. and Roth, A. (2009)
Erdil, A. and Ergin, H. (2008)
Ergin, H. (2002)
Ergin, H. and Sonmez, T. (2006)
Kesten, O. (2010)
Presentation 4 Applications (3) - Kidney Exchange 7/3
Sonmez, T. and Unver, U. (2013) --- Ryota Ohata
Ashlagi, I. and Roth, A. (2012) --- Pan Cong
References
**Sonmez, T. and Unver, U. (2013)
*Roth, A., Sonmez, T. and Unver, U. (2005)
*Roth, A., Sonmez, T. and Unver, U. (2007)
Ashlagi, I. and Roth, A. (2012)
Roth, A., Sonmez, T. and Unver, U. (2004)
Unver, U. (2010)
Presentation 5 Matching with Contracts 7/10
Hatfield, J. and Milgrom, P. (2005) --- Zhou Yu
References
**Hatfield, J. and Milgrom, P. (2005)
*Aygun, O. and Sonmez, T. (2013)
Echenique, F. (2012)
Presentation 6 Unraveling 7/17
Avery, C. and Levin, J. (2010) --- Yuuki Ryono
Halaburda, H. (2010) --- Takashi Ogawa
References
Avery, C. and Levin, J. (2010)
Coles, P., Cawley, J., Levine, P., Niederle, M., Roth, A., and Siegfried, J. (2010)
Frechette, G., Roth, A. and Utku U. (2007)
Halaburda, H. (2010)
Li, H. and Rosen, S. (1998)
Niederle, M. and Roth, A. (2003b)
Roth, A. and Xing, X. (1994)
Backup Various Matching Market Design
Course Bidding
Dynamic Assignment
Position Auctions
US Military Academy
References
Budish, E. and Cantillon, E. (2012)
Edelman, B., Ostrovsky, M., and Schwarz, M. (2007)
Kennes, J., Monte, D. and Tumennasan, N. (2013)
Kurino, M. (2014)
Pereyra, J. (2013)
Sonmez, T. (2013)
Sonmez, T. and Switzer, T. (2013)
Varian, H. (2007)
Backup Frontier of School Choice Problems
To be written...
References
**Abdulkadiroglu, A. Che, Y.-K. and Yasuda, Y. (2008)
**Abdulkadiroglu, A. Che, Y.-K. and Yasuda, Y. (2011)
*Pathak, P. and Sonmez, T. (2008)
*Pathak, P. and Sonmez, T. (2013)
Goto, M. et al. (2014)
Hafalir, I., Yenmez, B. and Yildrim, M. (2013)
Monte, D. and Tumennasan, N. (2013)
Pathak, P. and Sethuraman, J. (2011)
Backup Connection to Non-Cooperative Games
To be written...
References
**Kandori, M., Kojima, F., and Yasuda, Y. (2008)
*Echenique, F. (2004)
*Hatfield, J. and Milgrom, P. (2005)
Alcadem, J. (1996)
Echenique, F. (2003)
Echenique, F. (2007)
Echenique, F. and Oviedo, J. (2006)
Kara, T. and Sonmez, T. (1996)
Sotomayor, M. (2004)
Sotomayor, M. (2007)
Backup Other Theoretical Issues
Discrete Mathematics
Externalities
Econometrics
Networks
Non-Substitutable Preference
References
Bando, K. (2012)
Echenique, F., Lee, S., Yenmez, B. and Shum, M. (2013)
Eguchi, A., Fujishige, S. and Tamura, A. (2003)
Fleiner, T (2003)
Fujishige, S. and Tamura, A. (2007)
Hatfield, J. et al. (2013)
Ostrovsky, M. (2007)
Pycia, M. (2012)
Sasaki, H. and Toda, M. (1996)
Uetake, K. and Watanabe, Y. (2012)
Westkamp, A. (2010)
Papers on Matching Market Design
Abdulkadiroglu, A., Che, Y.-K. and Yasuda, Y. (2011), Resolving Conflicting Preferences in School Choice: the "Boston Mechanism" Reconsidered, American Economic Review, 101: 399-410.
Abdulkadiroglu, A., Che, Y.-K. and Yasuda, Y. (2008), Expanding "Choice" in School Choice, American Economic Journal: Microeconomics, forthcoming.
Abdulkadiroglu, A., Pathak, P. and Roth, A. (2009), Strategy-proofness vs. Efficiency in Matching with Indifferences: Redesigning the NYC Match, American Economic Review, 99: 1954-1978.
Abdulkadiroglu, A. and Sonmez, T. (2003), School choice: a mechanism design approach, American Economic Review, 93: 729-747.
Abdulkadiroglu, A. and Sonmez, T. (2013), Matching Markets: Theory and Practice, in Advances in Economics and Econometrics Tenth World Congress, Edited by Daron Acemoglu, Manuel Arellano, Eddie Dekel.
Adachi, H. (2000), On a characterization of stable matchings, Economics Letters, 68: 43–49.
Alcalde, J. (1996), Implementation of Stable Solutions to Marriage Problems, Journal of Economic Theory, 69: 240–254.
Alcalde, J. and Barbera, S. (1994), Top dominance and the possibility of strategy-proof stable solutions to matching problems, Economic Theory, 4: 417-435.
Ashlagi, I. and Roth, A. (2012), New challenges in multi-hospital kidney exchange, American Economic Review (P&P), 102: 354-359.
Avery, C. and Levin, J. (2010), Early Admissions at Selective Colleges, American Economic Review, 100: 2125-2156
Aygun, O. and Sonmez, T. (2013), Matching with Contracts: Comment, American Economic Review, 103: 2050-2051.
Balinski M and Sonmez, T. (1999), A tale of two mechanisms: student placement, Journal of Economic Theory, 84: 73–94.
Bando, K. (2012), Many-to-one matching markets with externalities among firms, Journal of Mathematical Economics, 48: 14–20.
Blair, C. (1988), The Lattice Structure of the Set of Stable Matchings with Multiple Partners, Mathematics of Operations Research, 13: 619-628.
Bogomolnaia, A. and Moulin, H. (2001), A New Solution to the Random Assignment Problem, Journal of Economic Theory, 100: 295-328.
Budish, E. and Cantillon, E. (2012), The Multi-Unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard, American Economic Review, 102: 2237-2271.
Bulow, J. and Levin, J. (2006), Matching and price competition, American Economic Review, 96: 652–668.
Coles, P., Cawley, J., Levine, P., Niederle, M., Roth, A., and Siegfried, J. (2010), The Job Market for New Economists: A Market Design Perspective, Journal of Economic Perspectives, 24: 187-206.
Crawford, V. and Knoer, E. (1981), Job Matching with Heterogeneous Firms and Workers, Econometrica, 49: 437-450.
Demange, G. and Gale, D. (1985), The Strategy Structure of Two-Sided Matching Markets, Econometrica, 53: 873-888.
Demange, G., Gale, D. and Sotomayor, M. (1987), A further note on the stable matching problem, Discrete Applied Mathematics, 16: 217–222.
Dubins, L. and Freedman, D. (1981), Machiavelli and the Gale-Shapley algorithm, American Mathematics Monthly, 88: 485–494/
Echenique, F. (2003), The Equilibrium Set of a Two Player Game with Complementarities is a Sublattice, Economic Theory, 22: 903-905.
Echenique, F. (2004), A Characterization of Strategic Complementarities, Games and Economic Behavior, 46: 325-347.
Echenique, F. (2005), A Short And Constructive Proof of Tarski's Fixed-Point Theorem, International Journal of Game Theory, 33: 215-218.
Echenique, F. (2007), Finding All Equilibria in Games with Strategic Complements, Journal of Economic Theory, 135: 514-532.
Echenique, F. (2012), Contracts vs. Salaries in Matching, American Economic Review, 102: 594-601.
Echenique, F., Lee, S., Yenmez, B. and Shum, M. (2013), The Revealed Preference Theory of Stable and Extremal Stable Matchings, Econometrica, 81: 153-171.
Echenique, F. and Oviedo, J. (2004), Core many-to-one matchings by fixed point methods, Journal of Economic Theory, 115: 358–376.
Echenique, F. and Oviedo, J. (2006), A theory of stability in many-to-many matching markets, Theoretical Economics, 1: 233–273.
Economic Sciences Prize Committee of the Royal Swedish Academy of Sciences (2012), Stable Allocations and The Practice of Market Design, Scientific Background on the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2012. Link
Edelman, B., Ostrovsky, M., and Schwarz, M. (2007), Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars of Keywords, American Economic Review, 97: 242-259.
Eguchi, A., Fujishige, S. and Tamura, A. (2003), A Generalized Gale-Shapley Algorithm for a Discrete-Concave Stable-Marriage Model, in Algorithms and Computation, edited by Ibaraki, T., Katoh, N. and Ono H., ISAAC2003, Lecture Notes in Computer Science 2906, Springer, 495-504.
Erdil, A. and Ergin, H. (2008), What's the Matter with Tie-Breaking? Improving Efficiency in School Choice, American Economic Review, 98: 669-689.
Ergin, H. (2002), Efficient resource allocation on the basis of priorities, Econometrica, 70: 2489–2497.
Ergin, H. and Sonmez, T. (2006), Games of school choice under the Boston mechanism, Journal of Public Economics, 90: 215–237.
Fleiner, T (2003), A fixed-point approach to stable matchings and some applications, Mathematics of Operations Research, 28: 103–126.
Frechette, G.., Roth, A. and Utku U. (2007), Unraveling yields inefficient matchings: evidence from post-season college football bowls, RAND Journal of Economics, 38: 967–982.
Fujishige, S. and Tamura, A. (2007), A Two-Sided Discrete-Concave Market with Possibly Bounded Side Payments: An Approach by Discrete Convex Analysis, Mathematics of Operations Research, 32: 136-155.
Gale, D. and Shapley, L. (1962), College Admissions and the Stability of Marriage, American Mathematical Monthly, 69: 9-15.
Gale, D and Sotomayor, M. (1985a), Some remarks on the stable matching problem, Discrete Applied Mathematics, 11: 223-32.
Gale, D and Sotomayor, M. (1985b), Ms Machiavelli and the stable matching problem, American Mathematical Monthly, 92: 261-8.
Goto, M., Hashimoto, N., Iwasaki, A., Kawasaki, Y., Ueda, S., Yasuda, Y. and Yokoo, M. (2014), Strategy-proof Matching with Regional Minimum Quotas, AAMAS2014 (Full Paper), forthcoming.
Hafalir, I., Yenmez, B. and Yildrim, M. (2013), Effective Affirmative Action in School Choice, Theoretical Economics, 8: 325-363.
Halaburda, H. (2010), Unravelling in Two-Sided Matching Markets and Similarity of Preferences, Games and Economic Behavior, 69: 365-393.
Hatfield, J., Kominers, S., Nichifor, A., Ostrovsky, M. and Westkamp, A. (2013), Stability and Competitive Equilibrium in Trading Networks, Journal of Political Economy, 121: 966-1005.
Hatfield, J. and Milgrom, P. (2005), Matching with Contracts, American Economic Review, 95: 913-935.
Hylland, A. and Zeckhauser, R. (1977), The efficient allocation of individuals to positions, Journal of Political Economy, 87: 293-314.
Kara, T. and Sonmez, T. (1996), Nash Implementation of Matching Rules, Journal of Economic Theory, 68: 425–439.
Kandori, M., Kojima, F., and Yasuda, Y. (2008), Understanding Stable Matchings: A Non-Cooperative Approach, mimeo.
Kelso, A. and Crawford, V. (1982), Job Matching, Coalition Formation, and Gross Substitutes, Econometrica, 50: 1483-1504.
Kennes, J., Monte, D. and Tumennasan, N. (2013), The Daycare Assignment: A Dynamic Matching Problem, American Economic Journal: Microeconomics, forthcoming.
Kesten, O. (2010), School Choice with Consent, Quarterly Journal of Economics, 125: 1297-1348.
Knuth, D. (1976), Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms, English Reprint (1996).
Kojima, F. and Pathak, P. (2009), Incentives and Stability in Large Two-Sided Matching Markets, American Economic Review, 99: 608-627.
Kojima, F., Pathak, P., and Roth, A. (2013), Stability and Incentives in Matching with Couples, Quarterly Journal of Economics, 128: 1585-1632.
Kojima, F. and Troyan, P. (2011), Matching and Market Design: An Introduction to Selected Topics, Japanese Economic Review, 62: 82–98.
Kurino, M. (2014), House Allocation with Overlapping Generations, American Economic Journal: Microeconomics, 6: 258–289.
Levin, J. (2013), The Economics of Internet Markets, in Advances in Economics and Econometrics Tenth World Congress, Edited by Daron Acemoglu, Manuel Arellano, Eddie Dekel.
Li, H. and Rosen, S. (1998), Unraveling in Matching Markets, American Economic Review, 88: 371-387.
Ma, J. (1994), Strategy-Proofness and the Strict Core in a Market with Indivisibilities, International Journal of Game Theory, 23: 75-83.
Milgrom, P. (2004), Putting Auction Theory to Work.
Milgrom, P. and Roberts, J. (1990), Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities, Econometrica, 58: 1255-1277.
Milgrom, P. and Roberts, J. (1994), Comparing Equilibria, American Economic Review, 84: 441-459.
Mongell, S. and Roth, A. (1986), A Note on Job Matching with Budget Constraints, Economics Letters, 21: 135-138.
Mongell, S. and Roth, A. (1991), Sorority Rush as a Two-Sided Matching Mechanism, American Economic Review, 81: 441-464.
Monte, D. and Tumennasan, N. (2013), Matching with quorums, Economics Letters, 120: 14–17.
Niederle, M. and Roth, A. (2003a), Relationship Between Wages and Presence of a Matching in Medical Fellowships, Journal of the American Medical Associations, 290: 1153-1154.
Niederle, M. and Roth, A. (2003b), Unraveling Reduces the Scope of an Entry Level Labor Market: Gastroentrology with and without a Centralized Match, Journal of Political Economy, 111: 1342-1352.
Niederle, M., Roth, A. and Sonmez, T. (2008), Matching, in The New Palgrave Dictionary of Economics, edited by Steven N. Durlauf and Lawrence E. Blume.
Ostrovsky, M. (2007), Stability in Supply-Chain Networks, American Economic Review, 98: 897-923.
Pathak, P. and Sethuraman, J. (2011), Lotteries in Student Assignment: An Equivalence Result, Theoretical Economics, 6: 1-18.
Pathak, P. and Sonmez, T. (2008), Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism, American Economic Review, 98: 1636-1652.
Pathak, P. and Sonmez, T. (2013), School Admissions Reform in Chicago and England: Comparing Mechanisms by their Vulnerability to Manipulation, American Economic Review, 103: 80-106.
Pereyra, J. (2013), A Dynamic School Choice Model, Games and Economic Behavior, 80: 100–114.
Pycia, M. (2012), Stability and Preference Alignment in Matching and Coalition Formation, Econometrica, 80: 323-362.
Quinzii, M. (1984), Core and Competitive Equilibria with Indivisibilities, International Journal of Game Theory, 13: 41-60.
Roth, A. (1982), The economics of matching: stability and incentives, Mathematics of Operations Research, 7: 617-28.
Roth, A. (1984a), The evolution of the labor market for medical interns and residents: a case study in game theory, Journal of Political Economy, 92: 991–1016.
Roth, A. (1984b), Stability and Polarization of Interests in Job Matching, Econometrica, 52: 47-58.
Roth, A. (1985), The college admissions problem is not equivalent to the marriage problem, Journal of Economic Theory, 36: 277–288.
Roth, A. (1986), On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets, Econometrica, 54: 425-427.
Roth, A. (1991), A Natural Experiment in the Organization of Entry Level Labor Markets: Regional Markets for New Physicians and Surgeons in the U.K, American Economic Review, 81: 415-440.
Roth, A. (2002), The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics, Econometrica, 70: 1341-1378.
Roth, A. (2003), The Origins, History, and Design of the Resident Match, Journal of the American Medical Association, 289 :909-912.
Roth, A. (2008a), What Have We Learned from Marked Design?, Economic Journal, 118: 285-310.
Roth, A. (2008b), Deferred acceptance algorithms: history, theory, practice, and open questions, International Journal of Game Theory, 36: 537-569.
Roth, A. and Peranson, E. (1999), The redesign of the matching market for American physicians: some engineering aspects of economic design, American Economic Review, 89: 748–780.
Roth, A. and Postlewaite, A. (1977), Weak Versus Strong Domination in a Market with Indivisible Goods, Journal of Mathematical Economics, 4: 131-137.
Roth, A. and Rothblum, U. (1999), Truncation Strategies in Matching Markets - in Search of Advice for Participants, Econometrica, 67: 21-43.
Roth, A., Sonmez, T. and Unver, U. (2003), Kidney Exchange, Quarterly Journal of Economics, 119: 457-488.
Roth, A., Sonmez, T. and Unver, U. (2005), Pairwise Kidney Exchange, Journal of Economic Theory, 125: 151-188.
Roth, A., Sonmez, T. and Unver, U. (2007), Efficient Kidney Exchange: Coincidence of Wants in a Market with Compatibility-Based Preferences, American Economic Review, 97: 828–851.
Roth, A. and Sotomayor, M. (1989), The College Admissions Problem Revisited, Econometrica, 57: 559-70.
Roth, A. and Vande Vate, J. (1990), Random Paths to Stability in Two-Sided Matching, Econometrica, 58: 1475-1480.
Roth, A. and Xing, X. (1994), Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions, American Economic Review, 84: 992-1044.
Sasaki, H. and Toda, M. (1996), Two-Sided Matching Problems with Externalities, Journal of Economic Theory, 70: 93–108.
Shapley, L. and Shubik, M. (1971), The assignment game I: the core, International Journal of Game Theory, 1:111–130.
Shapley, L. and Scarf, H. (1974), On cores and indivisibility, Journal of Mathematical Economics, 1:23–28.
Sonmez, T. (2013), Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism, Journal of Political Economy, 121: 186-219.
Sonmez, T. and Switzer, T. (2013), Matching with (Branch-of-Choice) Contracts at the United States Military Academy, Econometrica, 81: 451-488.
Sonmez, T. and Unver, U. (2005), House allocation with existing tenants: an equivalence, Games and Economic Behavior, 52:153–185.
Sonmez, T. and Unver, U. (2011), Matching, Allocation, and Exchange of Discrete Resources, in Handbook of Social Economics, Vol. 1A, edited by J. Benhabib, A. Bisin, and M. Jackson.
Sonmez, T. and Unver, U. (2013), Market Design for Kidney Exchange, in Handbook of Market Design, edited by Z. Neeman, A. Roth, N. Vulkan.
Sotomayor, M. (1996), A non constructive elementary proof of the existence of stable marriages, Games and Economic Behavior, 13: 135–7.
Sotomayor, M. (1999), Three remarks on the many-to-many stable matching problem: Dedicated to David Gale on his 75th birthday, Mathematical Social Sciences, 38: 55–70.
Sotomayor, M. (2004), Implementation in the many-to-many matching market, Games and Economic Behavior, 46: Pages 199–212.
Sotomayor, M. (2007), Connecting the cooperative and competitive structures of the multiple-partners assignment game, Journal of Economic Theory, 134: 155–174.
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