IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v36y2007i1p17-26.html
   My bibliography  Save this article

A simple procedure to obtain the extreme core allocations of an assignment market

Author

Listed:
  • Josep Izquierdo
  • Marina Núñez
  • Carles Rafels

Abstract

Given an assignment market, we introduce a set of vectors, one for each possible ordering on the player set, which we name the max-payoff vectors. Each one of these vectors is obtained recursively only making use of the assignment matrix. Those max-payoff vectors that are efficient turn up to give the extreme core allocations of the market. When the assignment market has large core (that is to say, the assignment matrix is dominant diagonal and doubly dominant diagonal) all the max-payoff vectors are extreme core allocations.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Josep Izquierdo & Marina Núñez & Carles Rafels, 2007. "A simple procedure to obtain the extreme core allocations of an assignment market," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 17-26, September.
    • Handle: RePEc:spr:jogath:v:36:y:2007:i:1:p:17-26
    DOI: 10.1007/s00182-007-0091-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00182-007-0091-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00182-007-0091-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Pere Villar, Joan, 2002. "Assignment Games Satisfy the CoMa-Property," Games and Economic Behavior, Elsevier, vol. 38(2), pages 231-239, February.
    2. 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.
    3. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
    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.
    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. Marina Núñez & Tamás Solymosi, 2017. "Lexicographic allocations and extreme core payoffs: the case of assignment games," Annals of Operations Research, Springer, vol. 254(1), pages 211-234, July.
    2. Grabisch, Michel & Sudhölter, Peter, 2018. "On a class of vertices of the core," Games and Economic Behavior, Elsevier, vol. 108(C), pages 541-557.
    3. Takaaki Abe & Shuige Liu, 2018. "Monotonic Core Allocation Paths for Assignment Games," Working Papers 1808, Waseda University, Faculty of Political Science and Economics.
    4. Marina Núñez, 2016. "Comments on: Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 327-329, July.
    5. Michel Grabisch, 2016. "Rejoinder on: Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 335-337, July.
    6. 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.
    7. Takaaki Abe & Shuige Liu, 2019. "Monotonic core allocation paths for assignment games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 557-573, December.
    8. Ata Atay & Marina N'u~nez & Tam'as Solymosi, 2024. "A many-to-one job market: more about the core and the competitive salaries," Papers 2404.04847, arXiv.org.
    9. 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.
    10. Martínez-de-Albéniz, F. Javier & Núñez, Marina & Rafels, Carles, 2011. "Assignment markets with the same core," Games and Economic Behavior, Elsevier, vol. 73(2), pages 553-563.
    11. Michel Grabisch, 2016. "Rejoinder on: Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 335-337, July.
    12. Saadia El Obadi & Silvia Miquel, 2019. "Assignment Games with a Central Player," Group Decision and Negotiation, Springer, vol. 28(6), pages 1129-1148, December.

    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. 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.
    2. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
    3. 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.
    4. Marina Núñez & Tamás Solymosi, 2017. "Lexicographic allocations and extreme core payoffs: the case of assignment games," Annals of Operations Research, Springer, vol. 254(1), pages 211-234, July.
    5. Marina Núñez & Carles Rafels, 2004. "Bargained stable allocations in assignment markets," Working Papers 153, Barcelona School of Economics.
    6. Martínez-de-Albéniz, F. Javier & Núñez, Marina & Rafels, Carles, 2011. "Assignment markets with the same core," Games and Economic Behavior, Elsevier, vol. 73(2), pages 553-563.
    7. Oriol Tejada, 2013. "Analysis of the core of multisided Böhm-Bawerk assignment markets," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 189-205, April.
    8. Takaaki Abe & Shuige Liu, 2019. "Monotonic core allocation paths for assignment games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 557-573, December.
    9. F. Javier Martínez-de-Albéniz & Carlos Rafels & Neus Ybern, 2018. "Solving Becker's assortative assignments and extensions," UB School of Economics Working Papers 2018/376, University of Barcelona School of Economics.
    10. Adegbesan, Tunji, 2007. "Strategic factor markets: Bargaining, scarcity, and resource complementarity," IESE Research Papers D/666, IESE Business School.
    11. Marina Núñez & Carles Rafels, 2009. "Von Neumann-Morgenstern stable-set solutions in the assignment market," Working Papers 412, Barcelona School of Economics.
    12. 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.
    13. 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.
    14. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
    15. Marina Núñez & Carles Rafels, 2006. "A Canonical Representation for the Assignment Game: the Kernel and the Nucleolus," Working Papers 279, Barcelona School of Economics.
    16. 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.
    17. Martínez-de-Albéniz, F. Javier & Rafels, Carlos & Ybern, Neus, 2019. "Solving Becker's assortative assignments and extensions," Games and Economic Behavior, Elsevier, vol. 113(C), pages 248-261.
    18. Keisuke Bando & Yakuma Furusawa, 2023. "The minimum set of $$\mu $$ μ -compatible subgames for obtaining a stable set in an assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 231-252, March.
    19. Bolle, Friedel & Breitmoser, Yves & Otto, Philipp E., 2011. "A positive theory of cooperative games: The logit core and its variants," MPRA Paper 32918, University Library of Munich, Germany.
    20. Kucuksenel, Serkan, 2011. "Core of the assignment game via fixed point methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 72-76, January.

    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:spr:jogath:v:36:y:2007:i:1:p:17-26. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.