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Matching with partners and projects

Author

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  • Nicolò, Antonio
  • Sen, Arunava
  • Yadav, Sonal

Abstract

We propose a model where agents are matched in pairs in order to undertake a project. Agents have preferences over both the partner and the project they are assigned to. These preferences over partners and projects are separable and dichotomous. Each agent partitions the set of partners into friends and outsiders, and the set of projects into good and bad ones. Friendship is mutual and transitive. In addition, preferences over projects among friends are correlated (homophily). We define a suitable notion of the weak core and propose an algorithm, the minimum demand priority algorithm (MDPA) that generates an assignment in the weak core. In general, the strong core does not exist but the MDPA assignment satisfies a limited version of the strong core property when only friends can be members of the blocking coalition. The MDPA is also strategy-proof. Finally we show that our assumptions on preferences are indispensable. We show that the weak core may fail to exist if any of the assumptions of homophily, separability and dichotomous preferences are relaxed.

Suggested Citation

  • Nicolò, Antonio & Sen, Arunava & Yadav, Sonal, 2019. "Matching with partners and projects," Journal of Economic Theory, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jetheo:v:184:y:2019:i:c:s002205311830214x
    DOI: 10.1016/j.jet.2019.104942
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    References listed on IDEAS

    as
    1. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    2. Alkan, Ahmet, 1988. "Nonexistence of stable threesome matchings," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 207-209, October.
    3. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    4. Justin Burkett & Francis X. Flanagan & Amanda L. Griffith, 2018. "Allocating group housing," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(4), pages 581-596, April.
    5. Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January.
    6. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," Working Papers 261, Barcelona School of Economics.
    7. Jens Gudmundsson, 2014. "When do stable roommate matchings exist? A review," Review of Economic Design, Springer;Society for Economic Design, vol. 18(2), pages 151-161, June.
    8. , & , J., 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    9. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
    10. John William Hatfield & Scott Duke Kominers, 2012. "Matching in Networks with Bilateral Contracts," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 176-208, February.
    11. Bettina Klaus & Flip Klijn & Jordi Massó, 2007. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," Review of Economic Design, Springer;Society for Economic Design, vol. 11(3), pages 175-184, November.
    12. Donald Boyd & Hamilton Lankford & Susanna Loeb & James Wyckoff, 2013. "Analyzing the Determinants of the Matching of Public School Teachers to Jobs: Disentangling the Preferences of Teachers and Employers," Journal of Labor Economics, University of Chicago Press, vol. 31(1), pages 83-117.
    13. Benjamin Golub & Matthew O. Jackson, 2012. "How Homophily Affects the Speed of Learning and Best-Response Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1287-1338.
    14. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    15. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    16. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    17. Morimitsu Kurino, 2014. "House Allocation with Overlapping Generations," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 258-289, February.
    18. Marek Pycia, 2012. "Stability and Preference Alignment in Matching and Coalition Formation," Econometrica, Econometric Society, vol. 80(1), pages 323-362, January.
    19. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 153-170.
    20. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    21. , & ,, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
    22. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    23. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    24. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    25. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    26. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    27. Gaurav, Abhishek & Picot, Jérémy & Sen, Arunava, 2017. "The decomposition of strategy-proof random social choice functions on dichotomous domains," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 28-34.
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    Cited by:

    1. Yoshio Sano & Ping Zhan, 2021. "Extended Random Assignment Mechanisms on a Family of Good Sets," SN Operations Research Forum, Springer, vol. 2(4), pages 1-30, December.
    2. Combe, Julien, 2022. "Matching with ownership," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    3. Nicolò, Antonio & Salmaso, Pietro & Sen, Arunava & Yadav, Sonal, 2023. "Stable sharing," Games and Economic Behavior, Elsevier, vol. 141(C), pages 337-363.

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    More about this item

    Keywords

    Matching; Stability; Strategy-proofness; Two-sided matching; One-sided matching;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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