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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

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

    as
    1. 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.
    2. 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.
    3. 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.
    4. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    6. Thomson, William, 1983. "Problems of fair division and the Egalitarian solution," Journal of Economic Theory, Elsevier, vol. 31(2), pages 211-226, December.
    7. 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.
    8. 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.
    9. 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.
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    Cited by:

    1. Béal, Sylvain & Casajus, André & Huettner, Frank & Rémila, Eric & Solal, Philippe, 2014. "Solidarity within a fixed community," Economics Letters, Elsevier, vol. 125(3), pages 440-443.
    2. Calleja, Pere & Llerena Garrés, Francesc, 2018. "Weak fairness and the Shapley value," Working Papers 2072/306979, Universitat Rovira i Virgili, Department of Economics.
    3. 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.
    4. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2017. "Duality in land rental problems," MPRA Paper 80509, University Library of Munich, Germany.
    5. repec:kap:theord:v:83:y:2017:i:3:d:10.1007_s11238-017-9604-1 is not listed on IDEAS
    6. Sylvain Béal & Eric Rémila & Phillippe Solal, 2017. "Coalitional desirability and the equal division value," Working Papers 2017-08, CRESE.

    More about this item

    Keywords

    TU-game; Equal division solution; CIS-value; ENSC-value; Population solidarity; Consistency;

    JEL classification:

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

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