IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v33y2016i01ns021759591650007x.html
   My bibliography  Save this article

Cooperative Fuzzy Games with Convex Combination Form

Author

Listed:
  • Fanyong Meng

    (School of Business, Central South University, Changsha 410083, P. R. China)

  • Xiaohong Chen

    (School of Business, Central South University, Changsha 410083, P. R. China†School of Accounting, Hunan University of Commerce, Changsha 410205, P. R. China)

Abstract

In this paper, a new class of cooperative fuzzy games named fuzzy games with convex combination form is introduced. This kind of fuzzy games considers two aspects of information. One is the contribution of the players to the associated crisp coalitions; the other is their participation levels. The explicit expression of the Shapley function is given, which is equal to the production of the Shapley function on crisp games and the player participation levels. Meanwhile, the relationship between the fuzzy core and the Shapley function is studied. Surprisingly, the relationship between them does coincide as in crisp case. Furthermore, some desirable properties are researched. Finally, an example is provided to illustrate the difference in fuzzy coalition values and the player Shapley values for four types of fuzzy games.

Suggested Citation

  • Fanyong Meng & Xiaohong Chen, 2016. "Cooperative Fuzzy Games with Convex Combination Form," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-25, February.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:01:n:s021759591650007x
    DOI: 10.1142/S021759591650007X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021759591650007X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021759591650007X?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. Chunqiao Tan & Zhong-Zhong Jiang & Xiaohong Chen, 2013. "Choquet Extension Of Cooperative Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-20.
    2. Liu, Jiuqiang & Tian, Hai-Yan, 2014. "Existence of fuzzy cores and generalizations of the K–K–M–S theorem," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 148-152.
    3. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    4. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    5. Neog, Rupok & Borkotokey, Surajit, 2011. "Dynamic resource allocation in fuzzy coalitions : a game theoretic model," MPRA Paper 40074, University Library of Munich, Germany.
    6. Butnariu, Dan & Kroupa, Tomas, 2008. "Shapley mappings and the cumulative value for n-person games with fuzzy coalitions," European Journal of Operational Research, Elsevier, vol. 186(1), pages 288-299, April.
    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. Liu, Zhi & Zheng, Xiao-Xue & Li, Deng-Feng & Liao, Chen-Nan & Sheu, Jiuh-Biing, 2021. "A novel cooperative game-based method to coordinate a sustainable supply chain under psychological uncertainty in fairness concerns," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    2. ShinichiIshihara & Junnosuke Shino, 2023. "An AxiomaticAnalysisofIntervalShapleyValues," Working Papers 2214, Waseda University, Faculty of Political Science and Economics.

    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. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Discussion Paper 2002-13, Tilburg University, Center for Economic Research.
    2. Fanyong Meng & Qiang Zhang & Xiaohong Chen, 2017. "Fuzzy Multichoice Games with Fuzzy Characteristic Functions," Group Decision and Negotiation, Springer, vol. 26(3), pages 565-595, May.
    3. Fanyong Meng & Xiaohong Chen & Chunqiao Tan, 2016. "Cooperative fuzzy games with interval characteristic functions," Operational Research, Springer, vol. 16(1), pages 1-24, April.
    4. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    5. Dall'Aglio, M. & Brânzei, R. & Tijs, S.H., 2008. "Cooperation in Dividing the Cake," Discussion Paper 2008-101, Tilburg University, Center for Economic Research.
    6. Casajus, André & Huettner, Frank, 2015. "Potential, value, and the multilinear extension," Economics Letters, Elsevier, vol. 135(C), pages 28-30.
    7. Cristina Fernández & Peter Borm & Ruud Hendrickx & Stef Tijs, 2005. "Drop out monotonic rules for sequencing situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 501-504, July.
    8. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Games, MDPI, vol. 8(4), pages 1-25, November.
    9. Norde, Henk & Moretti, Stefano & Tijs, Stef, 2004. "Minimum cost spanning tree games and population monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 154(1), pages 84-97, April.
    10. D. Kilgour & Terrence Levesque, 1984. "The Canadian constitutional amending formula: Bargaining in the past and the future," Public Choice, Springer, vol. 44(3), pages 457-480, January.
    11. Serguei Kaniovski, 2008. "The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 281-300, August.
    12. Xin Jiang & Yuyu Liu & Ranhang Zhao, 2019. "A Framework for Ecological Compensation Assessment: A Case Study in the Upper Hun River Basin, Northeast China," Sustainability, MDPI, vol. 11(4), pages 1-13, February.
    13. Marichal, Jean-Luc & Mathonet, Pierre & Spizzichino, Fabio, 2015. "On modular decompositions of system signatures," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 19-32.
    14. Vito Fragnelli & Gianfranco Gambarelli, 2014. "Further open problems in cooperative games," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(4), pages 51-62.
    15. van den Brink, René & Núñez, Marina & Robles, Francisco, 2021. "Valuation monotonicity, fairness and stability in assignment problems," Journal of Economic Theory, Elsevier, vol. 195(C).
    16. Ehlers, Lars, 2003. "Multiple public goods, lexicographic preferences, and single-plateaued preference rules," Games and Economic Behavior, Elsevier, vol. 43(1), pages 1-27, April.
    17. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Convex Games Versus Clan Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 363-372.
    18. Richard P. McLean & Amit Pazgal & William W. Sharkey, 2004. "Potential, Consistency, and Cost Allocation Prices," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 602-623, August.
    19. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    20. Németh, Tibor & Pintér, Miklós, 2017. "The non-emptiness of the weak sequential core of a transferable utility game with uncertainty," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 1-6.

    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:wsi:apjorx:v:33:y:2016:i:01:n:s021759591650007x. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.