IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v58y2009i2p202-213.html
   My bibliography  Save this article

Values of games with graph restricted communication and a priori unions

Author

Listed:
  • Alonso-Meijide, J.M.
  • Álvarez-Mozos, M.
  • Fiestras-Janeiro, M.G.

Abstract

Two new values for transferable utility games with graph restricted communication and a priori unions are introduced and characterized. Moreover, a comparison between these and the Owen graph value is provided. These values are used to analyze the distribution of power in the Basque Parliament emerging from elections in April 2005.

Suggested Citation

  • Alonso-Meijide, J.M. & Álvarez-Mozos, M. & Fiestras-Janeiro, M.G., 2009. "Values of games with graph restricted communication and a priori unions," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 202-213, September.
    • Handle: RePEc:eee:matsoc:v:58:y:2009:i:2:p:202-213
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(09)00058-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    References listed on IDEAS

    as
    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 137-141.
    3. Vazquez-Brage, Margarita & Garcia-Jurado, Ignacio & Carreras, Francesc, 1996. "The Owen Value Applied to Games with Graph-Restricted Communication," Games and Economic Behavior, Elsevier, vol. 12(1), pages 42-53, January.
    4. Amer, Rafael & Carreras, Francese & Gimenez, Jose Miguel, 2002. "The modified Banzhaf value for games with coalition structure: an axiomatic characterization," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 45-54, January.
    5. José Alonso-Meijide & M. Fiestras-Janeiro, 2002. "Modification of the Banzhaf Value for Games with a Coalition Structure," Annals of Operations Research, Springer, vol. 109(1), pages 213-227, January.
    6. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    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. Oriol Tejada & Mikel Álvarez-Mozos, 2017. "Games with Graph Restricted Communication and Levels Structure of Cooperation," UB School of Economics Working Papers 2017/363, University of Barcelona School of Economics.
    2. Caulier, Jean-François & Mauleon, Ana & Vannetelbosch, Vincent, 2015. "Allocation rules for coalitional network games," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 80-88.
    3. J. M. Alonso-Meijide & M. Álvarez-Mozos & M. G. Fiestras-Janeiro, 2017. "Power Indices and Minimal Winning Coalitions for Simple Games in Partition Function Form," Group Decision and Negotiation, Springer, vol. 26(6), pages 1231-1245, November.
    4. Zijun Li & Fanyong Meng, 2023. "The α-Egalitarian Myerson value of games with communication structure," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 311-338, June.
    5. José María Alonso-Meijide & Mikel Álvarez-Mozos & María Gloria Fiestras-Janeiro, 2015. "Power Indices and Minimal Winning Coalitions in Simple Games with Externalities Abstract: We propose a generalization of simple games to situations with coalitional externalities. The main novelty of ," UB School of Economics Working Papers 2015/328, University of Barcelona School of Economics.
    6. Sylvain Béal & Sylvain Ferrières & Eric Rémila & Philippe Solal, 2017. "Axiomatic and bargaining foundation of an allocation rule for ordered tree TU-games," Post-Print halshs-01644797, HAL.
    7. Wenrong Lyu & Erfang Shan & Zeguang Cui, 2024. "Consistency of the Owen value for TU-games with coalition and graph structures," Annals of Operations Research, Springer, vol. 338(2), pages 991-1017, July.
    8. René Brink & Gerard Laan & Nigel Moes, 2015. "Values for transferable utility games with coalition and graph structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 77-99, April.
    9. Tejada, O. & Álvarez-Mozos, M., 2018. "Graphs and (levels of) cooperation in games: Two ways how to allocate the surplus," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 114-122.
    10. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "Axiomatization of an allocation rule for ordered tree TU-games," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 132-140.
    11. Sylvain Béal & Eric Rémila & Philippe Solal, 2022. "Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 818-849, May.
    12. Kongo, Takumi, 2011. "Value of games with two-layered hypergraphs," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 114-119, September.
    13. Erfang Shan, 2023. "Marginality and a Characterization of the Owen Graph value," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 451-461, June.
    14. Jilei Shi & Lei Cai & Erfang Shan & Wenrong Lyu, 2022. "A value for cooperative games with coalition and probabilistic graph structures," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 646-671, April.
    15. Rene van den Brink & Gerard van der Laan & Nigel Moes, 2011. "Two Values for Transferable Utility Games with Coalition and Graph Structure," Tinbergen Institute Discussion Papers 11-164/1, Tinbergen Institute.
    16. Erfang Shan & Jilei Shi & Wenrong Lyu, 2023. "The efficient partition surplus Owen graph value," Annals of Operations Research, Springer, vol. 320(1), pages 379-392, January.

    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. Tejada, O. & Álvarez-Mozos, M., 2018. "Graphs and (levels of) cooperation in games: Two ways how to allocate the surplus," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 114-122.
    2. van den Brink, Rene & van der Laan, Gerard, 2005. "A class of consistent share functions for games in coalition structure," Games and Economic Behavior, Elsevier, vol. 51(1), pages 193-212, April.
    3. Sylvain Béal & Eric Rémila & Philippe Solal, 2022. "Allocation rules for cooperative games with restricted communication and a priori unions based on the Myerson value and the average tree solution," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 818-849, May.
    4. J. Alonso-Meijide & B. Casas-Méndez & A. González-Rueda & S. Lorenzo-Freire, 2014. "Axiomatic of the Shapley value of a game with a priori unions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 749-770, July.
    5. Oriol Tejada & Mikel Álvarez-Mozos, 2017. "Games with Graph Restricted Communication and Levels Structure of Cooperation," UB School of Economics Working Papers 2017/363, University of Barcelona School of Economics.
    6. Meng, Fanyong & Chen, Xiaohong & Zhang, Qiang, 2015. "A coalitional value for games on convex geometries with a coalition structure," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 605-614.
    7. Wenrong Lyu & Erfang Shan & Zeguang Cui, 2024. "Consistency of the Owen value for TU-games with coalition and graph structures," Annals of Operations Research, Springer, vol. 338(2), pages 991-1017, July.
    8. Jilei Shi & Erfang Shan, 2021. "The Banzhaf value for generalized probabilistic communication situations," Annals of Operations Research, Springer, vol. 301(1), pages 225-244, June.
    9. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    10. Kongo, Takumi, 2011. "Value of games with two-layered hypergraphs," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 114-119, September.
    11. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
    12. Sylvain Béal & Anna Khmelnitskaya & Philippe Solal, 2018. "Two-step values for games with two-level communication structure," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 563-587, February.
    13. M. Álvarez-Mozos & O. Tejada, 2015. "The Banzhaf value in the presence of externalities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 781-805, April.
    14. Elena Parilina & Artem Sedakov, 2016. "Stable Cooperation in a Game with a Major Player," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-20, June.
    15. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring Power and Satisfaction in Societies with Opinion Leaders," PSE-Ecole d'économie de Paris (Postprint) hal-00756720, HAL.
    16. Caulier, Jean-François & Mauleon, Ana & Vannetelbosch, Vincent, 2015. "Allocation rules for coalitional network games," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 80-88.
    17. Stefano Benati & Giuseppe Vittucci Marzetti, 2021. "Voting power on a graph connected political space with an application to decision-making in the Council of the European Union," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 733-761, November.
    18. van den Brink, J.R., 1999. "An Axiomatization of the Shapley Value Using a Fairness Property," Other publications TiSEM 0090365c-9bab-4367-b660-5, Tilburg University, School of Economics and Management.
    19. René Brink & Anna Khmelnitskaya & Gerard Laan, 2016. "An Owen-type value for games with two-level communication structure," Annals of Operations Research, Springer, vol. 243(1), pages 179-198, August.
    20. Ichiro Nishizaki & Tomohiro Hayashida & Yuki Shintomi, 2016. "A core-allocation for a network restricted linear production game," Annals of Operations Research, Springer, vol. 238(1), pages 389-410, March.

    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:eee:matsoc:v:58:y:2009:i:2:p:202-213. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.