IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v21y2013i3p572-589.html
   My bibliography  Save this article

The collective value: a new solution for games with coalition structures

Author

Listed:
  • Yoshio Kamijo

Abstract

In this study, we provide a new solution for cooperative games with coalition structures. The collective value of a player is defined as the sum of the equal division of the pure surplus obtained by his coalition from the coalitional bargaining and of his Shapley value for the internal coalition. The weighted Shapley value applied to a game played by coalitions with coalition-size weights is assigned to each coalition, reflecting the size asymmetries among coalitions. We show that the collective value matches exogenous interpretations of coalition structures and provide an axiomatic foundation of this value. A noncooperative mechanism that implements the collective value is also presented. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:21:y:2013:i:3:p:572-589
    DOI: 10.1007/s11750-011-0191-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11750-011-0191-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11750-011-0191-y?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 search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Gérard Hamiache, 2006. "A value for games with coalition structures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 93-105, January.
    3. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    4. Vidal-Puga, Juan & Bergantinos, Gustavo, 2003. "An implementation of the Owen value," Games and Economic Behavior, Elsevier, vol. 44(2), pages 412-427, August.
    5. Levy, Anat & Mclean, Richard P., 1989. "Weighted coalition structure values," Games and Economic Behavior, Elsevier, vol. 1(3), pages 234-249, September.
    6. 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.
    7. Calvo, Emilio & Javier Lasaga, J. & Winter, Eyal, 1996. "The principle of balanced contributions and hierarchies of cooperation," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 171-182, June.
    8. 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).
    9. Kamijo, Yoshio, 2008. "Implementation of weighted values in hierarchical and horizontal cooperation structures," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 336-349, November.
    10. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    11. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 227-240.
    12. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    13. Casajus, André, 2009. "Outside options, component efficiency, and stability," Games and Economic Behavior, Elsevier, vol. 65(1), pages 49-61, January.
    14. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    15. R. Amer & F. Carreras, 1995. "Cooperation indices and coalitional value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 117-135, June.
    16. Yoshio Kamijo, 2009. "A Two-Step Shapley Value For Cooperative Games With Coalition Structures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 207-214.
    17. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Hou, Dongshuang & Sun, Hao & Sun, Panfei & Driessen, Theo, 2018. "A note on the Shapley value for airport cost pooling game," Games and Economic Behavior, Elsevier, vol. 108(C), pages 162-169.
    2. Abe, Takaaki & Nakada, Satoshi, 2023. "The in-group egalitarian Owen values," Games and Economic Behavior, Elsevier, vol. 142(C), pages 1-16.
    3. Gérard Hamiache, 2012. "A Matrix Approach to TU Games with Coalition and Communication Structures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 85-100, January.
    4. Xun-Feng Hu & Gen-Jiu Xu & Deng-Feng Li, 2019. "The Egalitarian Efficient Extension of the Aumann–Drèze Value," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1033-1052, June.
    5. Besner, Manfred, 2020. "Values for level structures with polynomial-time algorithms, relevant coalition functions, and general considerations," MPRA Paper 99355, University Library of Munich, Germany.
    6. 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.
    7. 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.
    8. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    9. 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.
    10. Yokote, Koji & Kongo, Takumi & Funaki, Yukihiko, 2018. "The balanced contributions property for equal contributors," Games and Economic Behavior, Elsevier, vol. 108(C), pages 113-124.
    11. 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.
    12. Xun-Feng Hu & Deng-Feng Li, 2021. "The Equal Surplus Division Value for Cooperative Games with a Level Structure," Group Decision and Negotiation, Springer, vol. 30(6), pages 1315-1341, December.
    13. Rong Zou & Wenzhong Li & Marc Uetz & Genjiu Xu, 2023. "Two-step Shapley-solidarity value for cooperative games with coalition structure," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 1-25, March.

    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. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Balanced per capita contributions and level structure of cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 167-176, July.
    2. Vidal-Puga, Juan, 2012. "The Harsanyi paradox and the “right to talk” in bargaining among coalitions," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 214-224.
    3. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    4. Xun-Feng Hu & Gen-Jiu Xu & Deng-Feng Li, 2019. "The Egalitarian Efficient Extension of the Aumann–Drèze Value," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1033-1052, June.
    5. Silvia Lorenzo-Freire, 2017. "New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 579-600, October.
    6. 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.
    7. María Gómez-Rúa & Juan Vidal-Puga, 2014. "Bargaining and membership," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 800-814, July.
    8. Rong Zou & Genjiu Xu & Wenzhong Li & Xunfeng Hu, 2020. "A coalitional compromised solution for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 735-758, December.
    9. Abe, Takaaki, 2024. "Equal surplus sharing values for games with coalition structures," Economics Letters, Elsevier, vol. 240(C).
    10. Xun-Feng Hu, 2021. "New axiomatizations of the Owen value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 585-603, June.
    11. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    12. Manfred Besner, 2022. "Harsanyi support levels solutions," Theory and Decision, Springer, vol. 93(1), pages 105-130, July.
    13. Besner, Manfred, 2018. "Weighted Shapley hierarchy levels values," MPRA Paper 88160, University Library of Munich, Germany.
    14. André Casajus & Rodrigue Tido Takeng, 2022. "Second-order productivity, second-order payoffs, and the Owen value," Post-Print hal-03798448, HAL.
    15. 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.
    16. Jun Su & Yuan Liang & Guangmin Wang & Genjiu Xu, 2020. "Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    17. Besner, Manfred, 2018. "Two classes of weighted values for coalition structures with extensions to level structures," MPRA Paper 87742, University Library of Munich, Germany.
    18. Calvo, Emilio & Gutiérrez, Esther, 2010. "Solidarity in games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 196-203, November.
    19. Besner, Manfred, 2022. "The grand surplus value and repeated cooperative cross-games with coalitional collaboration," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    20. André Casajus & Rodrigue Tido Takeng, 2023. "Second-order productivity, second-order payoffs, and the Owen value," Annals of Operations Research, Springer, vol. 320(1), pages 1-13, 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:topjnl:v:21:y:2013:i:3:p:572-589. 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.