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Bipartite choices

Author

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  • Marco LiCalzi

    (Università Ca’ Foscari Venezia)

Abstract

This piece in the Milestones series is dedicated to the paper coauthored by David Gale and Lloyd Shapley and published in 1962 under the title “College admissions and the stability of marriage” on the American Mathematical Monthly.

Suggested Citation

  • Marco LiCalzi, 2022. "Bipartite choices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 551-568, December.
    • Handle: RePEc:spr:decfin:v:45:y:2022:i:2:d:10.1007_s10203-022-00380-z
    DOI: 10.1007/s10203-022-00380-z
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    References listed on IDEAS

    as
    1. Baccara, Mariagiovanna & Lee, SangMok & Yariv, Leeat, 2020. "Optimal dynamic matching," Theoretical Economics, Econometric Society, vol. 15(3), July.
    2. Alkan, Ahmet, 1988. "Nonexistence of stable threesome matchings," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 207-209, October.
    3. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    4. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    5. Gale, David, 2009. "Topological games at Princeton, a mathematical memoir," Games and Economic Behavior, Elsevier, vol. 66(2), pages 647-656, July.
    6. Doval, Laura, 2022. "Dynamically stable matching," Theoretical Economics, Econometric Society, vol. 17(2), May.
    7. Roth, Alvin E., 2003. "The origins, history, and design of the resident match," Scholarly Articles 35059715, Harvard University Department of Economics.
    8. Enrico Maria Fenoaltea & Izat B. Baybusinov & Jianyang Zhao & Lei Zhou & Yi-Cheng Zhang, 2021. "The Stable Marriage Problem: an Interdisciplinary Review from the Physicist's Perspective," Papers 2103.11458, arXiv.org.
    9. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    10. David K Levine, 2018. "Introduction to Special Issue in Honor of Lloyd Shapley: Seven Topics in Game Theory," Levine's Working Paper Archive 786969000000001474, David K. Levine.
    11. Alvin E. Roth, 1985. "Conflict and Coincidence of Interest in Job Matching: Some New Results and Open Questions," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 379-389, August.
    12. Joshua S. Gans & George B. Shepherd, 1994. "How Are the Mighty Fallen: Rejected Classic Articles by Leading Economists," Journal of Economic Perspectives, American Economic Association, vol. 8(1), pages 165-179, Winter.
    13. Vulkan, Nir & Roth, Alvin E. & Neeman, Zvika (ed.), 2013. "The Handbook of Market Design," OUP Catalogue, Oxford University Press, number 9780199570515.
    14. Alvin E. Roth, 2018. "Marketplaces, Markets, and Market Design," American Economic Review, American Economic Association, vol. 108(7), pages 1609-1658, July.
    15. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    16. Marzena Rostek & Nathan Yoder, 2020. "Matching With Complementary Contracts," Econometrica, Econometric Society, vol. 88(5), pages 1793-1827, September.
    17. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    18. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    19. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    20. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    21. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    22. Alvin E. Roth & Robert B. Wilson, 2019. "How Market Design Emerged from Game Theory: A Mutual Interview," Journal of Economic Perspectives, American Economic Association, vol. 33(3), pages 118-143, Summer.
    23. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    24. Michael Greinecker & Christopher Kah, 2021. "Pairwise Stable Matching in Large Economies," Econometrica, Econometric Society, vol. 89(6), pages 2929-2974, November.
    25. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    26. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    27. David Gale, 2001. "The Two-Sided Matching Problem: Origin, Development And Current Issues," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 237-252.
    28. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    29. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
    30. Sobel, Joel, 2009. "ReGale: Some memorable results," Games and Economic Behavior, Elsevier, vol. 66(2), pages 632-642, July.
    31. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    32. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    33. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
    34. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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    More about this item

    Keywords

    Two-sided matching; Stable marriage problem; College admission problem; Bipartite graph;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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