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Consistency, population solidarity, and egalitarian solutions for TU-games

Author

Listed:
  • René Brink

    (VU University)

  • Youngsub Chun

    (Seoul National University)

  • Yukihiko Funaki

    (Waseda University)

  • Boram Park

    (Ajou 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. The first class consists of all convex combinations of the equal division solution (which allocates the worth of the ‘grand coalition’ consisting of all players equally over all players) and the center-of-gravity of the imputation-set value (which first assigns every player its singleton worth and then allocates the remainder of the worth of the grand coalition, N, equally over all players). The second class is the dual class consisting of all convex combinations of the equal division solution and the egalitarian non-separable contribution value (which first assigns every player its contribution to the ‘grand coalition’ and then allocates the remainder equally over all players). We provide characterizations of the two classes of solutions using either population solidarity or a reduced game consistency in addition to other standard properties.

Suggested Citation

  • René Brink & Youngsub Chun & Yukihiko Funaki & Boram Park, 2016. "Consistency, population solidarity, and egalitarian solutions for TU-games," Theory and Decision, Springer, vol. 81(3), pages 427-447, September.
    • Handle: RePEc:kap:theord:v:81:y:2016:i:3:d:10.1007_s11238-016-9538-z
    DOI: 10.1007/s11238-016-9538-z
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    References listed on IDEAS

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    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.
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    6. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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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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