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Cooperative Games (Von Neumann-Morgenstern Stable Sets)

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Encyclopedia of Complexity and Systems Science

Glossary

Abstract game :

An abstract game consists of a set of outcomes and a binary relation, called domination, on the outcomes. Von Neumann and Morgenstern presented this game form for general applications of stable sets.

Characteristic function form game :

A characteristic function form game consists of a set of players and a characteristic function that gives each group of players, called a coalition, a value or a set of payoff vectors that they can gain by themselves. It is a typical representation of cooperative games. For characteristic function form games, several solution concepts are defined such as von Neumann-Morgenstern stable set, core, bargaining set, kernel, nucleolus, and Shapley value.

Domination :

Domination is a binary relation defined on the set of imputations, outcomes, or strategy combinations, depending on the form of a given game. In characteristic function form games, an imputation is said to dominate another imputation if there is a coalition of players such...

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Acknowledgments

This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant Numbers JP16H03121 and JP17K13696.

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Authors and Affiliations

  1. Department of Industrial Engineering and Economics, School of Engineering, Tokyo Institute of Technology, Tokyo, Japan

    Ryo Kawasaki

  2. Department of Economics, Gakushuin University, Tokyo, Japan

    Jun Wako

  3. Department of Business Economics, School of Management, Tokyo University of Science, Tokyo, Japan

    Shigeo Muto

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  1. Ryo Kawasaki
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  2. Jun Wako
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  3. Shigeo Muto
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Correspondence to Ryo Kawasaki .

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    Robert A. Meyers

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Kawasaki, R., Wako, J., Muto, S. (2018). Cooperative Games (Von Neumann-Morgenstern Stable Sets). In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_99-3

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  1. Latest

    Cooperative Games (Von Neumann-Morgenstern Stable Sets)
    Published:
    10 April 2018

    DOI: https://doi.org/10.1007/978-3-642-27737-5_99-3

  2. Original

    Cooperative Games (von Neumann–Morgenstern Stable Sets)
    Published:
    30 November 2015

    DOI: https://doi.org/10.1007/978-3-642-27737-5_99-2

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