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The maximum and the addition of assignment games

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  • S. Miquel
  • M. Núñez

Abstract

In the framework of two-sided assignment markets, we first consider that among several markets, the players may choose where to trade. It is shown that the corresponding game, represented by the maximum of a finite set of assignment games, may not be balanced. Some conditions for balancedness are provided and, in that case, properties of the core are analyzed. Secondly, we consider that players may trade simultaneously in more than one market and then add the profits. The corresponding game, represented by the sum of a finite set of assignment games, is balanced. Moreover, under some conditions, the sum of the cores of two assignment games coincides with the core of the sum game.
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Suggested Citation

  • S. Miquel & M. Núñez, 2011. "The maximum and the addition of assignment games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 189-212, July.
    • Handle: RePEc:spr:topjnl:v:19:y:2011:i:1:p:189-212
    DOI: 10.1007/s11750-010-0135-y
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    References listed on IDEAS

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    1. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
    3. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
    4. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
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    Cited by:

    1. Ata Atay & Eric Bahel & Tamás Solymosi, 2023. "Matching markets with middlemen under transferable utility," Annals of Operations Research, Springer, vol. 322(2), pages 539-563, March.
    2. Ata Atay & Francesc Llerena & Marina Núñez, 2016. "Generalized three-sided assignment markets: core consistency and competitive prices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 572-593, October.
    3. Francesc Llerena & Marina Núñez & Carles Rafels, 2015. "An axiomatization of the nucleolus of assignment markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 1-15, February.

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    More about this item

    Keywords

    Assignment game; Core; Nucleolus; 91A12; 91A40;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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