IDEAS home Printed from https://ideas.repec.org/p/edj/ceauch/328.html
   My bibliography  Save this paper

Take-it-or-leave-it contracts in many-to-many matching markets

Author

Listed:
  • Antonio Romero-Medina
  • Matteo Triossi

Abstract

We study a class of sequential non-revelation mechanisms where hospitals make simultaneous take-it-or-leave-it o?ers to doctors that either accept or reject them. We show that the mechanisms in this class are equivalent. They (weakly) implement the set of stable allocations in subgame perfect equilibrium. When all preferences are substitutable, the set of equilibria of the mechanisms in the class forms a lattice. Our results reveal a first-mover advantage absent in the model without contracts. We apply our findings to centralize school admissions problems, and we show obtaining pairwise stable allocations is possible through the immediate acceptance mechanism.Economic Literature Classification Numbers: C78, D78. Key words: Keywords: Many-to-many, contracts, ultimatum games.

Suggested Citation

  • Antonio Romero-Medina & Matteo Triossi, 2017. "Take-it-or-leave-it contracts in many-to-many matching markets," Documentos de Trabajo 328, Centro de Economía Aplicada, Universidad de Chile.
    • Handle: RePEc:edj:ceauch:328
    as

    Download full text from publisher

    File URL: http://www.cea-uchile.cl/wp-content/uploads/doctrab/ASOCFILE120170306092350.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    2. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2010. "Constrained School Choice: An Experimental Study," American Economic Review, American Economic Association, vol. 100(4), pages 1860-1874, September.
    3. Triossi, Matteo, 2009. "Hiring mechanisms, application costs and stability," Games and Economic Behavior, Elsevier, vol. 66(1), pages 566-575, May.
    4. Kominers, Scott Duke, 2012. "On the correspondence of contracts to salaries in (many-to-many) matching," Games and Economic Behavior, Elsevier, vol. 75(2), pages 984-989.
    5. Alcalde, Jose & Romero-Medina, Antonio, 2005. "Sequential decisions in the college admissions problem," Economics Letters, Elsevier, vol. 86(2), pages 153-158, February.
    6. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics 3 Volume Hardback Set," Cambridge Books, Cambridge University Press, number 9781107017214.
    7. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
    8. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    9. Claus-Jochen Haake & Bettina Klaus, 2009. "Monotonicity and Nash implementation in matching markets with contracts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 393-410, December.
    10. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    11. Baumol, William J, 1982. "Contestable Markets: An Uprising in the Theory of Industry Structure," American Economic Review, American Economic Association, vol. 72(1), pages 1-15, March.
    12. Fonseca-Mairena, María Haydée & Triossi, Matteo, 2019. "Incentives and implementation in marriage markets with externalities," Economics Letters, Elsevier, vol. 185(C).
    13. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
    14. Klaus, Bettina & Klijn, Flip, 2017. "Non-revelation mechanisms for many-to-many matching: Equilibria versus stability," Games and Economic Behavior, Elsevier, vol. 104(C), pages 222-229.
    15. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 215-237, January.
    16. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016064, September.
    17. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    18. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics 3 Volume Paperback Set," Cambridge Books, Cambridge University Press, number 9781107628861, December.
    19. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    20. Tayfun Sönmez & Tobias B. Switzer, 2013. "Matching With (Branch‐of‐Choice) Contracts at the United States Military Academy," Econometrica, Econometric Society, vol. 81(2), pages 451-488, March.
    21. Guillaume Haeringer & Myrna Wooders, 2011. "Decentralized job matching," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 1-28, February.
    22. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107627314, September.
    23. Klaus, Bettina & Walzl, Markus, 2009. "Stable many-to-many matchings with contracts," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 422-434, July.
    24. Alcalde, Jose & Romero-Medina, Antonio, 2000. "Simple Mechanisms to Implement the Core of College Admissions Problems," Games and Economic Behavior, Elsevier, vol. 31(2), pages 294-302, May.
    25. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016040, September.
    26. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    27. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    28. Yenmez, M. Bumin, 2018. "A college admissions clearinghouse," Journal of Economic Theory, Elsevier, vol. 176(C), pages 859-885.
    29. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    30. Alcalde, José, 2018. "Beyond the Spanish MIR with consent: (Hidden) cooperation and coordination in matching," Games and Economic Behavior, Elsevier, vol. 110(C), pages 32-49.
    31. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 197-218.
    32. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107638105, September.
    33. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    34. Baron David & Kalai Ehud, 1993. "The Simplest Equilibrium of a Majority-Rule Division Game," Journal of Economic Theory, Elsevier, vol. 61(2), pages 290-301, December.
    35. Abizada, Azar, 2016. "Stability and incentives for college admissions with budget constraints," Theoretical Economics, Econometric Society, vol. 11(2), May.
    36. Mongell, Susan J. & Roth, Alvin E., 1986. "A note on job matching with budget constraints," Economics Letters, Elsevier, vol. 21(2), pages 135-138.
    37. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107016057, September.
    38. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    39. Marilda Sotomayor, 2003. "Reaching the core of the marriage market through a non-revelation matching mechanism," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 241-251, December.
    40. Romero-Medina, Antonio & Triossi, Matteo, 2014. "Non-revelation mechanisms in many-to-one markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 624-630.
    41. Alcalde, Jose & Perez-Castrillo, David & Romero-Medina, Antonio, 1998. "Hiring Procedures to Implement Stable Allocations," Journal of Economic Theory, Elsevier, vol. 82(2), pages 469-480, October.
    42. M. Bumin Yenmez, 2014. "College Admissions," GSIA Working Papers 2014-E24, Carnegie Mellon University, Tepper School of Business.
    43. Acemoglu,Daron & Arellano,Manuel & Dekel,Eddie (ed.), 2013. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9781107674165, September.
    44. 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.
    45. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    46. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-440, June.
    47. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    48. Sotomayor, Marilda, 2004. "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages 199-212, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ronald Fischer, 2017. "Efectos de la Reforma del Código de Aguas," Documentos de Trabajo 335, Centro de Economía Aplicada, Universidad de Chile.
    2. Klaus, Bettina & Klijn, Flip, 2017. "Non-revelation mechanisms for many-to-many matching: Equilibria versus stability," Games and Economic Behavior, Elsevier, vol. 104(C), pages 222-229.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    2. Alcalde, José, 2018. "Beyond the Spanish MIR with consent: (Hidden) cooperation and coordination in matching," Games and Economic Behavior, Elsevier, vol. 110(C), pages 32-49.
    3. Somouaoga Bonkoungou, 2021. "Decentralized college admissions under single application," Review of Economic Design, Springer;Society for Economic Design, vol. 25(1), pages 65-91, June.
    4. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    5. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186-219.
    6. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.
    7. Yasushi Kawase & Keisuke Bando, 2021. "Subgame perfect equilibria under the deferred acceptance algorithm," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 503-546, June.
    8. Antonio Romero-Medina & Matteo Triossi, 2021. "Two-sided strategy-proofness in many-to-many matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 105-118, March.
    9. Masahiro Goto & Fuhito Kojima & Ryoji Kurata & Akihisa Tamura & Makoto Yokoo, 2017. "Designing Matching Mechanisms under General Distributional Constraints," American Economic Journal: Microeconomics, American Economic Association, vol. 9(2), pages 226-262, May.
    10. Schlegel, Jan Christoph, 2020. "Equivalent choice functions and stable mechanisms," Games and Economic Behavior, Elsevier, vol. 123(C), pages 41-53.
    11. Yan Chen & Peter Cramton & John A. List & Axel Ockenfels, 2021. "Market Design, Human Behavior, and Management," Management Science, INFORMS, vol. 67(9), pages 5317-5348, September.
    12. Yuichiro Kamada & Fuhito Kojima, 2020. "Accommodating various policy goals in matching with constraints," The Japanese Economic Review, Springer, vol. 71(1), pages 101-133, January.
    13. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    14. Umut M. Dur & Scott Duke Kominers & Parag A. Pathak & Tayfun Sönmez, 2013. "The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice," NBER Working Papers 18981, National Bureau of Economic Research, Inc.
    15. 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.
    16. Nikhil Agarwal & Eric Budish, 2021. "Market Design," NBER Working Papers 29367, National Bureau of Economic Research, Inc.
    17. Jonathan Ma & Scott Duke Kominers, 2018. "Bundling Incentives in (Many-to-Many) Matching with Contracts," Harvard Business School Working Papers 19-011, Harvard Business School.
    18. Bó, Inácio & Hakimov, Rustamdjan, 2022. "The iterative deferred acceptance mechanism," Games and Economic Behavior, Elsevier, vol. 135(C), pages 411-433.
    19. Cao, Shutao, 2017. "Accounting for productivity growth in a small open economy: Sector-specific technological change and relative prices of trade," Working Paper Series 6203, Victoria University of Wellington, School of Economics and Finance.
    20. Yenmez, M. Bumin, 2018. "A college admissions clearinghouse," Journal of Economic Theory, Elsevier, vol. 176(C), pages 859-885.

    More about this item

    Keywords

    keywords: many-to-many; contracts; ultimatum games.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:edj:ceauch:328. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/ceuclcl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.