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Fuzzy TU Games and Their Classes

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  • Milan Mareš

Abstract

The classical theory of coalitional games with transferable utility is based on the assumption that all parameters of such games, including the expected pay-offs of coalitions, are exactly determined. In real cooperative situations, this assumption appears rather umealistic. Then the coalitional pay-offs, formally represented by the values of characteristic function of the game, cannot be represented by crisp real numbers. The fuzzy set and fuzzy quantity theory offers adequate tools for the modelling of vagueness connected with expected pay-offs. The model of TU coalitional game was investigated in numerous papers and summarized in [5J. In this paper we focuse our attention to the fact that fuzzy expected pay-offs of coalitions can be easily transformed into fuzziness connected with classes of the complete games. This transformation can be well defined and under simple assumptions also unique. This uniqueness of the relation between fuzzy pay-offs in TU games and fuzzy class of deterministic TU games generated by them is analyzed in the submitted paper.

Suggested Citation

  • Milan Mareš, 2001. "Fuzzy TU Games and Their Classes," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 8(13).
  • Handle: RePEc:czx:journl:v:8:y:2001:i:13:id:99
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    File URL: http://ces.utia.cas.cz/bulletin/index.php/bulletin/article/view/99
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    Keywords

    game; coalitional game; coalition; fuzzy pay-offs; fuzzy class of games;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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