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Weak Surplus Mononicity characterizes convex combination of egalitarian Shapley value and Consensus value

Author

Listed:
  • Koji Yokote

    (Graduate School of Economics, Waseda University)

  • Yukihiko Funaki

    (Faculty of Political Science and Economics, Waseda University)

Abstract

We deal with the problem of striking a balance between marginalism and egalitarianism in the class of TU cooperative games. Weintroduce a new axiom, Weak Surplus Monotonicity. It states that if the marginal contribution of a player increases, the worth of the grand coalition increases and the cooperative surplus increases, then the payoff of the player should also increase. We show that a solution satisfies Efficiency, Symmetry and Weak Surplus Monotonicity if and only if it is a convex combination of the Shapley value, the Equal division and the CIS value. By replacing the new axiom with a stronger axiom and taking the dual, we obtain 11 characterizations of solutions, including the results of Young (1985) or Casajus and Huettner (2014).

Suggested Citation

  • Koji Yokote & Yukihiko Funaki, 2015. "Weak Surplus Mononicity characterizes convex combination of egalitarian Shapley value and Consensus value," Working Papers 1504, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1504
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    References listed on IDEAS

    as
    1. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    2. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
    3. René Brink & Yukihiko Funaki & Yuan Ju, 2013. "Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 693-714, March.
    4. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    5. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
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    Cited by:

    1. Pedro Calleja & Francesc Llerena, 2017. "Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 197-220, January.
    2. Koji Yokote & Yukihiko Funaki, 2017. "Monotonicity implies linearity: characterizations of convex combinations of solutions to cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(1), pages 171-203, June.

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    More about this item

    Keywords

    TU game; Shapley value; Monotonicity; Axiomatization;
    All these keywords.

    JEL classification:

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

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