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Fuzzy TU Games and Their Classes


  • Milan Mareš


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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    References listed on IDEAS

    1. Dirk Tasche, 2004. "The single risk factor approach to capital charges in case of correlated loss given default rates," Papers cond-mat/0402390,, revised Feb 2004.
    2. Konstantin Belyaev & Aelita Belyaeva & Tomas Konecny & Jakub Seidler & Martin Vojtek, 2012. "Macroeconomic Factors as Drivers of LGD Prediction: Empirical Evidence from the Czech Republic," Working Papers 2012/12, Czech National Bank, Research Department.
    3. Acharya, Viral V. & Bharath, Sreedhar T. & Srinivasan, Anand, 2007. "Does industry-wide distress affect defaulted firms? Evidence from creditor recoveries," Journal of Financial Economics, Elsevier, vol. 85(3), pages 787-821, September.
    4. Jiri Witzany, 2011. "A Two Factor Model for PD and LGD Correlation," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 18(28).
    5. Jon Frye, 2000. "Depressing recoveries," Emerging Issues, Federal Reserve Bank of Chicago, issue Oct.
    6. Stefano Caselli & Stefano Gatti & Francesca Querci, 2008. "The Sensitivity of the Loss Given Default Rate to Systematic Risk: New Empirical Evidence on Bank Loans," Journal of Financial Services Research, Springer;Western Finance Association, vol. 34(1), pages 1-34, August.
    7. Seidler, Jakub & Horvath, Roman & Jakubík, Petr, 2009. "Estimating expected loss given default in an emerging market: the case of Czech Republic," Journal of Financial Transformation, Capco Institute, vol. 27, pages 103-107.
    8. De Graeve, F. & Kick, T. & Koetter, M., 2008. "Monetary policy and financial (in)stability: An integrated micro-macro approach," Journal of Financial Stability, Elsevier, vol. 4(3), pages 205-231, September.
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    More about this item


    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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