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Transfers and exchange-stability in two-sided matching problems

Author

Listed:
  • Emiliya Lazarova

    (University of East Anglia)

  • Peter Borm

    (Tilburg University)

  • Arantza Estévez-Fernández

    (Vrije Universiteit Amsterdam)

Abstract

In this paper we consider one-to-many matching problems where the preferences of the agents involved are represented by monetary reward functions. We characterize Pareto optimal matchings by means of contractual exchange stability and matchings of maximum total reward by means of compensational exchange stability. To conclude, we show that in going from an initial matching to a matching of maximum total reward, one can always provide a compensation schedule that will be ex-post stable in the sense that there will be no subset of agents who can all by deviation obtain a higher reward. The proof of this result uses the fact that the core of an associated compensation matching game with constraints is nonempty.

Suggested Citation

  • Emiliya Lazarova & Peter Borm & Arantza Estévez-Fernández, 2016. "Transfers and exchange-stability in two-sided matching problems," Theory and Decision, Springer, vol. 81(1), pages 53-71, June.
    • Handle: RePEc:kap:theord:v:81:y:2016:i:1:d:10.1007_s11238-015-9524-x
    DOI: 10.1007/s11238-015-9524-x
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    References listed on IDEAS

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    1. Emiliya Lazarova & Peter Borm & Bas Velzen, 2011. "Coalitional games and contracts based on individual deviations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 507-520, December.
    2. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    3. Dutta, Bhaskar & Masso, Jordi, 1997. "Stability of Matchings When Individuals Have Preferences over Colleagues," Journal of Economic Theory, Elsevier, vol. 75(2), pages 464-475, August.
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    5. Marek Pycia, 2012. "Stability and Preference Alignment in Matching and Coalition Formation," Econometrica, Econometric Society, vol. 80(1), pages 323-362, January.
    6. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 275-287, December.
    7. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    8. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.
    9. Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 567-583.
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    Cited by:

    1. Arantza Estévez-Fernández & José Manuel Giménez-Gómez & María José Solís-Baltadano, 2019. "Sequential bankruptcy problems," Tinbergen Institute Discussion Papers 19-076/II, Tinbergen Institute.
    2. Feng Zhang & Jing Li & Junxiang Fan & Huili Shen & Jian Shen & Hua Yu, 2019. "Three-dimensional stable matching with hybrid preferences," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 330-336, January.

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    More about this item

    Keywords

    Matching; Pareto optimal matching; Contractual exchange stability; Compensational stability; Compensation schedule;
    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
    • D60 - Microeconomics - - Welfare Economics - - - General

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