Optimal coalition formation and surplus distribution: Two sides of one coin

    Research output: Contribution to JournalArticleAcademicpeer-review

    Abstract

    A fuzzy coalitional game represents a situation in which players can vary the intensity at which they participate in the coalitions accessible to them, as opposed to the treatment as a binary choice in the non-fuzzy (crisp) game. Building on the property - not made use of so far in the literature of fuzzy games - that a fuzzy game can be represented as a convex program, this paper shows that the optimum of such a program determines the optimal coalitions as well as the optimal rewards for the players, two sides of one coin. Furthermore, this program is seen to provide a unifying framework for representing the core, the least core, and the (fuzzy) nucleolus, among others. Next, we derive conditions for uniqueness of core rewards and to deal with non-uniqueness we introduce a family of parametric perturbations of the convex program that encompasses a large number of well-known concepts for selection from the core, including the Dutta-Ray solution (Dutta and Ray, 1989), the equal sacrifice solution (Yu, 1973), the equal division solution (Selten, 1972) and the tau-value (Tijs, 1981). We also generalize the concept of the Grand Coalition of contracting players by allowing for multiple technologies, and we specify the conditions for this allocation to be unique and Egalitarian. Finally, we show that our formulation offers a natural extension to existing models of production economies with threats and division rules for common surplus. © 2011 Published by Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)604-615
    JournalEuropean Journal of Operational Research
    Volume215
    Issue number3
    DOIs
    Publication statusPublished - 2011

    Fingerprint

    Fuzzy Games
    Coalition Formation
    Coalitions
    Convex Program
    Reward
    Half line
    Division
    Coalitional Games
    Binary Choice
    Nucleolus
    Nonuniqueness
    Natural Extension
    Uniqueness
    Vary
    Game
    Perturbation
    Generalise
    Formulation
    Coalition formation
    Surplus

    Cite this

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    title = "Optimal coalition formation and surplus distribution: Two sides of one coin",
    abstract = "A fuzzy coalitional game represents a situation in which players can vary the intensity at which they participate in the coalitions accessible to them, as opposed to the treatment as a binary choice in the non-fuzzy (crisp) game. Building on the property - not made use of so far in the literature of fuzzy games - that a fuzzy game can be represented as a convex program, this paper shows that the optimum of such a program determines the optimal coalitions as well as the optimal rewards for the players, two sides of one coin. Furthermore, this program is seen to provide a unifying framework for representing the core, the least core, and the (fuzzy) nucleolus, among others. Next, we derive conditions for uniqueness of core rewards and to deal with non-uniqueness we introduce a family of parametric perturbations of the convex program that encompasses a large number of well-known concepts for selection from the core, including the Dutta-Ray solution (Dutta and Ray, 1989), the equal sacrifice solution (Yu, 1973), the equal division solution (Selten, 1972) and the tau-value (Tijs, 1981). We also generalize the concept of the Grand Coalition of contracting players by allowing for multiple technologies, and we specify the conditions for this allocation to be unique and Egalitarian. Finally, we show that our formulation offers a natural extension to existing models of production economies with threats and division rules for common surplus. {\circledC} 2011 Published by Elsevier B.V. All rights reserved.",
    author = "M.A. Keyzer and {van Wesenbeeck}, C.F.A.",
    year = "2011",
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    Optimal coalition formation and surplus distribution: Two sides of one coin. / Keyzer, M.A.; van Wesenbeeck, C.F.A.

    In: European Journal of Operational Research, Vol. 215, No. 3, 2011, p. 604-615.

    Research output: Contribution to JournalArticleAcademicpeer-review

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