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The alpha-constant-sum games

Author

Listed:
  • Wenna Wang

    (Northwestern Polytechnical University, VU University)

  • Rene van den Brink

    (VU University)

  • Hao Sun

    (Northwestern Polytechnical University)

  • Genjiu Xu

    (Northwestern Polytechnical University)

  • Zhengxing Zou

    (Beijing Institute of Technology, VU University, Amsterdam)

Abstract

Given any alpha in [0,1], an alpha-constant-sum game on a finite set of players, N, is a function that assigns a real number to any coalition S (being a subset of the player set N), such that the sum of the worth of the coalition S and the worth of its complementary coalition N\S is alpha times of the worth of the grand coalition N. This class contains the constant-sum games of Khmelnitskaya (2003) (for alpha = 1) and games of threats of Kohlberg and Neyman (2018) (for alpha = 0) as special cases. An alpha-constant-sum game may not be a classical TU cooperative game as it may fail to satisfy the condition that the worth of the empty set is 0, except when alpha = 1. In this paper, we will build a value theory for the class of alpha-constant-sum games, and mainly introduce the alpha-quasi-Shapley value. We characterize this value by classical axiomatizations for TU games. We show that axiomatizations of the equal division value do not work on these classes of alpha-constant-sum games.

Suggested Citation

  • Wenna Wang & Rene van den Brink & Hao Sun & Genjiu Xu & Zhengxing Zou, "undated". "The alpha-constant-sum games," Tinbergen Institute Discussion Papers 19-022/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20190022
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    References listed on IDEAS

    as
    1. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    2. Kohlberg, Elon & Neyman, Abraham, 2018. "Games of threats," Games and Economic Behavior, Elsevier, vol. 108(C), pages 139-145.
    3. René Brink & Yukihiko Funaki, 2015. "Implementation and axiomatization of discounted Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 329-344, September.
    4. Anna B. Khmelnitskaya, 2003. "Shapley value for constant-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 223-227, December.
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    More about this item

    Keywords

    alpha-constant-sum game; alpha-quasi-Shapley value; threat game; constant-sum-game;
    All these keywords.

    JEL classification:

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

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