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Generalized Cores And Stable Sets For Fuzzy Games

Author

Listed:
  • S. MUTO

    (Department of Value and Decision Science, Graduate School of Decision Science and Technology, Tokyo Institute of Technology, Japan)

  • S. ISHIHARA

    (Department of Value and Decision Science, Graduate School of Decision Science and Technology, Tokyo Institute of Technology, Japan)

  • E. FUKUDA

    (Department of Value and Decision Science, Graduate School of Decision Science and Technology, Tokyo Institute of Technology, Japan)

  • S. H. TIJS

    (Center and Department of Econometrics and Operations Research, Tilburg University, The Netherlands)

  • R. BRÂNZEI

    (Faculty of Computer Science, 'Alexandru Ioan Cuza' University, Iasi, Romania)

Abstract

Core elements (a la Aubin) of a fuzzy game can be associated with additive separable supporting functions of fuzzy games. Generalized cores whose elements consist of more general separable supporting functions of the game are introduced and studied. While the Aubin core of unanimity games can be empty, the generalized core of unanimity games is nonempty. Properties of the generalized cores and their relations to stable sets are studied. For convex fuzzy games interesting properties are found such as the fact that the generalized core is a unique generalized stable set.

Suggested Citation

  • S. Muto & S. Ishihara & E. Fukuda & S. H. Tijs & R. Brânzei, 2006. "Generalized Cores And Stable Sets For Fuzzy Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 95-109.
    • Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:01:n:s0219198906000801
    DOI: 10.1142/S0219198906000801
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    More about this item

    Keywords

    Cooperative game; core; stable set; decision making; fuzzy coalition; fuzzy game; dominance core; convex fuzzy game; 90D12; 03E72;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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