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A Value for Continuously-Many-Choice Cooperative Games

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  • Hsiao, Chih-Ru

Abstract

We extend a multi-choice cooperative game to a continuously-many-choice cooperative game. The set of all continuously-many-choice cooperative games is isomorphic to the set of all cooperative fuzzy games. A continuously-many-choice cooperative game and a cooperative fuzzy game have different physical interpretations. We define a value for the continuously-many-choice cooperative game and show that the value for the continuously-many-choice cooperative game has most properties as the traditional Shapley value does. Also, we give a probabilistic interpretation for the value. The probabilistic interpretation reveals some interesting properties of the value. Finally, we discuss the uniqueness of the value.

Suggested Citation

  • Hsiao, Chih-Ru, 1995. "A Value for Continuously-Many-Choice Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(3), pages 273-292.
    • Handle: RePEc:spr:jogath:v:24:y:1995:i:3:p:273-92
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    Cited by:

    1. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    2. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
    3. Hsiao, Chih-Ru, 2011. "A Review on Liao’s Dissertation Entitled “The Solutions on Multi-choice Games” and Related Publications," MPRA Paper 30260, University Library of Munich, Germany.
    4. Molina, Elisenda & Tejada, Juan, 2004. "Linear production games with committee control: Limiting behaviour of the core," European Journal of Operational Research, Elsevier, vol. 154(3), pages 609-625, May.

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