IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws133430.html
   My bibliography  Save this paper

The Shapley group value

Author

Listed:
  • Flores Díaz, Ramón Jesús
  • Molina, Elisenda
  • Tejada, Juan

Abstract

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person iteraction situation, we propose a group value, which we call the Shapley group value, as a priori evaluation of the prospects of a group of players in a coalitional game when acting as a unit. We study its properties and we give an axiomatic characterization. We motivate our proposal by means of some relevant applications of the Shapley group value, when it is used as an objective function by a decision maker who is trying to identify an optimal group of agents in a framework in which agents interact and the attained benefit can be modeled by means of a transferable utility game. As an illustrative example we analyze the problem of identifying the set of key agents in a terrorist network.

Suggested Citation

  • Flores Díaz, Ramón Jesús & Molina, Elisenda & Tejada, Juan, 2013. "The Shapley group value," DES - Working Papers. Statistics and Econometrics. WS ws133430, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws133430
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/17983/ws133430.pdf?sequence=1
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stefania Vitali & James B Glattfelder & Stefano Battiston, 2011. "The Network of Global Corporate Control," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-6, October.
    2. Rafael Amer & José Miguel Giménez, 2004. "A connectivity game for graphs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 453-470, December.
    3. Lindelauf, R.H.A. & Hamers, H.J.M. & Husslage, B.G.M., 2013. "Cooperative game theoretic centrality analysis of terrorist networks: The cases of Jemaah Islamiyah and Al Qaeda," European Journal of Operational Research, Elsevier, vol. 229(1), pages 230-238.
    4. Conklin, Michael & Powaga, Ken & Lipovetsky, Stan, 2004. "Customer satisfaction analysis: Identification of key drivers," European Journal of Operational Research, Elsevier, vol. 154(3), pages 819-827, May.
    5. 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).
    6. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    7. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    8. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    11. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    12. Roth, Alvin, 2012. "The Shapley Value as a von Neumann-Morgenstern Utility," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 1-9.
    13. Ilya Segal, 2003. "Collusion, Exclusion, and Inclusion in Random-Order Bargaining," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 439-460.
    14. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    15. Levy, Marc, 2011. "The Banzhaf index in complete and incomplete shareholding structures: A new algorithm," European Journal of Operational Research, Elsevier, vol. 215(2), pages 411-421, December.
    16. Michel Grabisch & Jacques Duchene & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Positions," Post-Print halshs-00273179, HAL.
    17. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    18. Albizuri, M.J., 2008. "Axiomatizations of the Owen value without efficiency," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 78-89, January.
    19. Crama, Yves & Leruth, Luc, 2007. "Control and voting power in corporate networks: Concepts and computational aspects," European Journal of Operational Research, Elsevier, vol. 178(3), pages 879-893, May.
    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. Flores Díaz, Ramón Jesús & Molina Ferragut, Elisenda & Tejada, Juan, 2014. "A game theoretic approach to group centrality," DES - Working Papers. Statistics and Econometrics. WS ws142215, Universidad Carlos III de Madrid. Departamento de Estadística.

    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. Ramón Flores & Elisenda Molina & Juan Tejada, 2019. "Evaluating groups with the generalized Shapley value," 4OR, Springer, vol. 17(2), pages 141-172, June.
    2. Casajus, André & Tutić, Andreas, 2013. "Nash bargaining, Shapley threats, and outside options," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 262-267.
    3. Calvo, Emilio & Lasaga, Javier & van den Nouweland, Anne, 1999. "Values of games with probabilistic graphs," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 79-95, January.
    4. Roger A McCain, 2013. "Value Solutions in Cooperative Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8528, January.
    5. Ramón Flores & Elisenda Molina & Juan Tejada, 2014. "Pyramidal values," Annals of Operations Research, Springer, vol. 217(1), pages 233-252, June.
    6. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    7. Giulia Cesari & Roberto Lucchetti & Stefano Moretti, 2017. "Generalized additive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 919-939, November.
    8. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    9. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    10. C. Manuel & E. González-Arangüena & R. Brink, 2013. "Players indifferent to cooperate and characterizations of the Shapley value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 1-14, February.
    11. Yoshio Kamijo, 2013. "The collective value: a new solution for games with coalition structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 572-589, October.
    12. Mayag, Brice & Bouyssou, Denis, 2020. "Necessary and possible interaction between criteria in a 2-additive Choquet integral model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 308-320.
    13. 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.
    14. Gerard van der Laan & René van den Brink, 2002. "A Banzhaf share function for cooperative games in coalition structure," Theory and Decision, Springer, vol. 53(1), pages 61-86, August.
    15. van den Brink, René & Pintér, Miklós, 2015. "On axiomatizations of the Shapley value for assignment games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 110-114.
    16. O. Tejada & M. Álvarez-Mozos, 2016. "Vertical syndication-proof competitive prices in multilateral assignment markets," Review of Economic Design, Springer;Society for Economic Design, vol. 20(4), pages 289-327, December.
    17. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    18. Bourheneddine Ben Dhaou & Abderrahmane Ziad, 2015. "The Free Solidarity Value," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201508, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    19. Agust'in G. Bonifacio & Elena Inarra & Pablo Neme, 2020. "Stable decompositions of coalition formation games," Papers 2009.11689, arXiv.org, revised Dec 2021.
    20. Armando Gomes, "undated". "A Theory of Negotiations and Formation of Coalitions," Rodney L. White Center for Financial Research Working Papers 21-99, Wharton School Rodney L. White Center for Financial Research.

    More about this item

    Keywords

    Game Theory;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:cte:wsrepe:ws133430. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.