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Consistency, Population Solidarity, and Egalitarian Solutions for TU-Games

Author

Listed:
  • Rene van den Brink

    (VU University Amsterdam)

  • Youngsub Chun

    (Seoul National University)

  • Yukihiko Funaki

    (Waseda University)

  • Boram Park

    (Rutgers University)

Abstract

A (point-valued) solution for cooperative games with transferable utility, or simply TU-games, assigns a payoff vector to every TU-game. In this paper we discuss two classes of equal surplus sharing solutions, one consisting of all convex combinations of the equal division solution and the CIS-value, and its dual class consisting of all convex combinations of the equal division solution and the ENSC-value. We provide several characterizations using either population solidarity or a reduced game consistency in addition to other standard properties.

Suggested Citation

  • Rene van den Brink & Youngsub Chun & Yukihiko Funaki & Boram Park, 2012. "Consistency, Population Solidarity, and Egalitarian Solutions for TU-Games," Tinbergen Institute Discussion Papers 12-136/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20120136
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    References listed on IDEAS

    as
    1. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    2. 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.
    3. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    4. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    5. 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.
    6. Youngsub Chun & Boram Park, 2012. "Population solidarity, population fair-ranking, and the egalitarian value," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 255-270, May.
    7. Yukihiko Funaki & Takehiko Yamato, 2001. "The Core And Consistency Properties: A General Characterisation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 175-187.
    8. 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.
    9. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    10. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    TU-game; equal division solution; CIS-value; ENSC-value; population solidarity; consistency;
    All these keywords.

    JEL classification:

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

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