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Dynamic resource allocation in fuzzy coalitions : a game theoretic model

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  • Neog, Rupok
  • Borkotokey, Surajit

Abstract

We introduce an efficient and dynamic resource allocation mechanism within the framework of a cooperative game with fuzzy coalitions. A fuzzy coalition in a resource allocation problem can be so defined that membership grades of the players in it, are proportional to the fractions of their total resources. We call any distribution of the resources possessed by the players, among a prescribed number of coalitions, a fuzzy coalition structure and every membership grade (equivalently fraction of the total resource), a resource investment. It is shown that this resource investment is influenced by satisfaction of the players in regards to better performance under a cooperative setup. Our model is based on the real life situations, where possibly one or more players compromise on their resource investments in order to help forming a coalition.

Suggested Citation

  • Neog, Rupok & Borkotokey, Surajit, 2011. "Dynamic resource allocation in fuzzy coalitions : a game theoretic model," MPRA Paper 40074, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:40074
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    References listed on IDEAS

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    1. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
    2. Debraj Ray and Rajiv Vohra, 1998. "Coalitional Power and Public Goods," Working Papers 98-24, Brown University, Department of Economics.
    3. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, December.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    6. Yaron Azrieli & Ehud Lehrer, 2007. "On some families of cooperative fuzzy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 1-15, September.
    7. Li, Shujin & Zhang, Qiang, 2009. "A simplified expression of the Shapley function for fuzzy game," European Journal of Operational Research, Elsevier, vol. 196(1), pages 234-245, July.
    8. Ronald R. Yager, 2007. "Multi-Agent Negotiation Using Linguistically Expressed Mediation Rules," Group Decision and Negotiation, Springer, vol. 16(1), pages 1-23, January.
    9. Surajit Borkotokey & Rupok Neog, 2012. "Allocating Profit Among Rational Players in a Fuzzy Coalition: A Game Theoretic Model," Group Decision and Negotiation, Springer, vol. 21(4), pages 439-459, July.
    10. Arnold, Tone & Schwalbe, Ulrich, 2002. "Dynamic coalition formation and the core," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 363-380, November.
    11. Debraj Ray & Rajiv Vohra, 2001. "Coalitional Power and Public Goods," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1355-1384, December.
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    Cited by:

    1. Yu-Hsien Liao, 2017. "Fuzzy games: a complement-consistent solution, axiomatizations and dynamic approaches," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 257-268, September.
    2. 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.

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    More about this item

    Keywords

    fuzzy coalitions; rational player; exact resource allocation; cooperative game;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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