IDEAS home Printed from https://ideas.repec.org/p/bge/wpaper/279.html
   My bibliography  Save this paper

A Canonical Representation for the Assignment Game: the Kernel and the Nucleolus

Author

Listed:
  • Marina Núñez
  • Carles Rafels

Abstract

The core of an assignment market is the translation, by the vector of minimum core payoffs, of the core of another better positioned market, the matrix of which has the properties of being dominant diagonal and doubly dominant diagonal. This new matrix is defined as the canonical form of the original assignment situation, and it is uniquely characterized by these three properties. The behavior of some well-known cooperative solutions in relation with the canonical form is analyzed. The kernel and the nucleolus of the assignment game, are proved to be the translation of the kernel and the nucleolus of the canonical representative by the vector of minimal core payoffs.

Suggested Citation

  • Marina Núñez & Carles Rafels, 2006. "A Canonical Representation for the Assignment Game: the Kernel and the Nucleolus," Working Papers 279, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:279
    as

    Download full text from publisher

    File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/279.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Theo S. H. Driessen, 1998. "A note on the inclusion of the kernel in the core of the bilateral assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 301-303.
    4. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    5. 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.
    6. 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.
    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. Trudeau, Christian, 2018. "From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution," Games and Economic Behavior, Elsevier, vol. 108(C), pages 225-238.

    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. Núñez, Marina & Rafels, Carles, 2009. "A glove-market partitioned matrix related to the assignment game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 598-610, November.
    2. 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.
    3. 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.
    4. Francesc Llerena (Universitat Rovira i Virgili - CREIP) & Marina Nunez (Universitat de Barcelona) & Carles Rafels (Universitat de Barcelona), 2012. "An axiomatization of the nucleolus of the assignment game," Working Papers in Economics 286, Universitat de Barcelona. Espai de Recerca en Economia.
    5. Oriol Tejada & Marina Núñez, 2012. "The nucleolus and the core-center of multi-sided Böhm-Bawerk assignment markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(2), pages 199-220, April.
    6. Núñez, Marina & Rafels, Carles, 2008. "On the dimension of the core of the assignment game," Games and Economic Behavior, Elsevier, vol. 64(1), pages 290-302, September.
    7. Heinrich Nax & Bary Pradelski, 2015. "Evolutionary dynamics and equitable core selection in assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 903-932, November.
    8. Francesc Llerena & Marina Nunez, 2011. "A geometric characterization of the nucleolus of the assignment game," Economics Bulletin, AccessEcon, vol. 31(4), pages 3275-3285.
    9. Tamas Solymosi & Balazs Sziklai, 2015. "Universal Characterization Sets for the Nucleolus in Balanced Games," CERS-IE WORKING PAPERS 1512, Institute of Economics, Centre for Economic and Regional Studies.
    10. Vijay V. Vazirani, 2022. "New Characterizations of Core Imputations of Matching and $b$-Matching Games," Papers 2202.00619, arXiv.org, revised Dec 2022.
    11. Tamás Solymosi, 2019. "Weighted nucleoli and dually essential coalitions (extended version)," CERS-IE WORKING PAPERS 1914, Institute of Economics, Centre for Economic and Regional Studies.
    12. Qizhi Fang & Bo Li & Xiaohan Shan & Xiaoming Sun, 2018. "Path cooperative games," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 211-229, July.
    13. R. Branzei & E. Gutiérrez & N. Llorca & J. Sánchez-Soriano, 2021. "Does it make sense to analyse a two-sided market as a multi-choice game?," Annals of Operations Research, Springer, vol. 301(1), pages 17-40, June.
    14. Tamás Solymosi, 2019. "Weighted nucleoli and dually essential coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1087-1109, December.
    15. Marina Nunez Oliva & Carlos Rafels Pallarola, 2005. "Uniform-price assignment markets," Working Papers in Economics 135, Universitat de Barcelona. Espai de Recerca en Economia.
    16. Arnold Polanski, 2016. "Matching structure and bargaining outcomes in buyer–seller networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 767-776, April.
    17. Tamás Solymosi, 2015. "The kernel is in the least core for permutation games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 795-809, December.
    18. Oriol Tejada & Carles Rafels, 2010. "Symmetrically multilateral-bargained allocations in multi-sided assignment markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 249-258, March.
    19. Ata Atay & Marina Núñez, 2019. "Multi-sided assignment games on m-partite graphs," Annals of Operations Research, Springer, vol. 279(1), pages 271-290, August.
    20. Adegbesan, Tunji, 2007. "Strategic factor markets: Bargaining, scarcity, and resource complementarity," IESE Research Papers D/666, IESE Business School.

    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:bge:wpaper:279. 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: Bruno Guallar (email available below). General contact details of provider: https://edirc.repec.org/data/bargses.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.