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The family of ideal values for cooperative games

Author

Listed:
  • Wenna Wang

    (Northwestern Polytechnical University, China)

  • Hao Sun

    (Northwestern Polytechnical University, China)

  • Rene (J.R.) van den Brink

    (VU University, Amsterdam, The Netherlands)

  • Genjiu Xu

    (Northwestern Polytechnical University, China)

Abstract

In view of the nature of pursuing profit, a selfish coefficient function is employed to describe the degrees of selfishness of players in different coalitions, which is the desired rate of return to the worth of coalitions. This function brings in the concept of individual expected reward to every player. Built on different selfish coefficient functions, the family of ideal values can be obtained by minimizing deviations from the individual expected rewards. Then we show the relationships between the family of ideal values and two other classical families of values: the procedural values and the least square values. For any selfish coefficient function m, the m-ideal value is characterized by efficiency, linearity, m-equal-expectation player property and nullifying player m-punishment property. We also provide an interpretation of a dynamic process for the m-ideal value. As two dual cases in the family of ideal values, the center-of-gravity of imputation-set value (CIS value) and the equal allocation of nonseparable costs value (EANS value) are raised from new axiomatic angles.

Suggested Citation

  • Wenna Wang & Hao Sun & Rene (J.R.) van den Brink & Genjiu Xu, 2018. "The family of ideal values for cooperative games," Tinbergen Institute Discussion Papers 18-002/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20180002
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    References listed on IDEAS

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    Cited by:

    1. Tiago Roux Oliveira & Victor Hugo Pereira Rodrigues & Miroslav Krstić & Tamer Başar, 2021. "Nash Equilibrium Seeking in Quadratic Noncooperative Games Under Two Delayed Information-Sharing Schemes," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 700-735, December.
    2. Xun-Feng Hu & Gen-Jiu Xu & Deng-Feng Li, 2019. "The Egalitarian Efficient Extension of the Aumann–Drèze Value," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1033-1052, June.
    3. Heidrich Balázs & Csákné Filep Judit & Mosolygó-Kiss Ágnes, 2018. "The war of the worlds? – A passing and taking of succession in Hungarian family businesses," Prosperitas, Budapest Business University, vol. 5(3), pages 8-23.
    4. José M. Alonso-Meijide & Julián Costa & Ignacio García-Jurado, 2019. "Null, Nullifying, and Necessary Agents: Parallel Characterizations of the Banzhaf and Shapley Values," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 1027-1035, March.

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    More about this item

    Keywords

    Game theory; m-Individual expected reward; The family of ideal values; Dynamic process; CIS and EANS values;
    All these keywords.

    JEL classification:

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

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