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A fundamental study for partially defined cooperative games

Author

Listed:
  • Satoshi Masuya

    (Daito Bunka University)

  • Masahiro Inuiguchi

    (Osaka University)

Abstract

The payoff of each coalition has been assumed to be known precisely in the conventional cooperative games. However, we may come across situations where some coalitional values remain unknown. This paper treats cooperative games whose coalitional values are not known completely. In the cooperative games it is assumed that some of coalitional values are known precisely but others remain unknown. Some complete games associated with such incomplete games are proposed. Solution concepts are studied in a special case where only values of the grand coalition and singleton coalitions are known. Through the investigations of solutions of complete games associated with the given incomplete game, we show a focal point solution suggested commonly from different viewpoints.

Suggested Citation

  • Satoshi Masuya & Masahiro Inuiguchi, 2016. "A fundamental study for partially defined cooperative games," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 281-306, September.
    • Handle: RePEc:spr:fuzodm:v:15:y:2016:i:3:d:10.1007_s10700-015-9229-1
    DOI: 10.1007/s10700-015-9229-1
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    References listed on IDEAS

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    1. David Housman, 2002. "Linear and symmetric allocation methods for partially defined cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 377-404.
    2. Itzhak Gilboa & David Schmeidler, 1992. "Additive Representation of Non-Additive Measures and the Choquet Integral," Discussion Papers 985, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    4. Theo Driessen & Anna Khmelnitskaya & Jordi Sales, 2012. "1-concave basis for TU games and the library game," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 578-591, October.
    5. Willson, Stephen J, 1993. "A Value for Partially Defined Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 371-384.
    6. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Jan Bok & Martin Černý, 2024. "1-convex extensions of incomplete cooperative games and the average value," Theory and Decision, Springer, vol. 96(2), pages 239-268, March.
    2. Yu-Hsien Liao, 2024. "Fuzzy Assessment Mechanisms under Multi-Objective Considerations," Mathematics, MDPI, vol. 12(19), pages 1-15, September.
    3. Satoshi Masuya, 2023. "Two Approaches to Estimate the Shapley Value for Convex Partially Defined Games," Mathematics, MDPI, vol. 12(1), pages 1-15, December.
    4. Martin Cerny & Michel Grabisch, 2023. "Player-centered incomplete cooperative games," Documents de travail du Centre d'Economie de la Sorbonne 23006, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Martin Černý & Jan Bok & David Hartman & Milan Hladík, 2024. "Positivity and convexity in incomplete cooperative games," Annals of Operations Research, Springer, vol. 340(2), pages 785-809, September.

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