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Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values

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  • René Brink

    ()

  • Yukihiko Funaki

    ()

  • Yuan Ju

    ()

Abstract

One of the main issues in economic allocation problems is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide three different characterizations of egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, from the perspective of a variable player set, we show that all these solutions satisfy the same reduced game consistency. Second, on a fixed player set, we characterize this class of solutions using monotonicity properties. Finally, towards a strategic foundation, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game. These characterizations discover fundamental differences as well as intriguing connections between marginalism and egalitarianism. Copyright The Author(s) 2013

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:40:y:2013:i:3:p:693-714
    DOI: 10.1007/s00355-011-0634-2
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    References listed on IDEAS

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    Cited by:

    1. Emilio Calvo & Esther Gutiérrez, 2012. "Weighted Solidarity Values," Discussion Papers in Economic Behaviour 0212, University of Valencia, ERI-CES.
    2. 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.
    3. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "A Class of Solidarity Allocation Rules for TU-games," Working Papers 2015-03, CRESE.
    4. Casajus, André & Yokote, Koji, 2017. "Weak differential marginality and the Shapley value," Journal of Economic Theory, Elsevier, vol. 167(C), pages 274-284.
    5. Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "A strategic implementation of the sequential equal surplus division rule for digraph cooperative games," Annals of Operations Research, Springer, vol. 253(1), pages 43-59, June.
    6. Marcin Malawski, 2013. "“Procedural” values for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 305-324, February.
    7. repec:spr:mathme:v:86:y:2017:i:1:d:10.1007_s00186-017-0587-z is not listed on IDEAS
    8. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2013. "A strategic implementation of the Average Tree solution for cycle-free graph games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2737-2748.
    9. Tadeusz Radzik & Theo Driessen, 2016. "Modeling values for TU-games using generalized versions of consistency, standardness and the null player property," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 179-205, April.
    10. Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "Axiomatization and implementation of a class of solidarity values for TU-games," Theory and Decision, Springer, vol. 83(1), pages 61-94, June.
    11. 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.
    12. 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.
    13. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    14. Tomohiko Kawamori, 2016. "Hart–Mas-Colell implementation of the discounted Shapley value," Theory and Decision, Springer, vol. 81(3), pages 357-369, September.
    15. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2015. "Non-manipulable rules for land rental problems," MPRA Paper 67334, University Library of Munich, Germany.
    16. 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.
    17. Emilio Calvo & Esther Gutiérrez-López, 2016. "A strategic approach for the discounted Shapley values," Theory and Decision, Springer, vol. 80(2), pages 271-293, February.
    18. Norman Kleinberg, 2015. "A note on the Sobolev consistency of linear symmetric values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 765-779, April.
    19. repec:spr:mathme:v:86:y:2017:i:2:d:10.1007_s00186-017-0595-z is not listed on IDEAS
    20. Sylvain Béal & Eric Rémila & Phillippe Solal, 2017. "Coalitional desirability and the equal division value," Working Papers 2017-08, CRESE.
    21. Wenna Wang & Hao Sun & Rene (J.R.) van den Brink & Genjiu Xu, 2018. "The family of ideal values for cooperative games," Tinbergen Institute Discussion Papers 18-002/II, Tinbergen Institute.
    22. repec:spr:joptap:v::y::i::d:10.1007_s10957-018-1259-8 is not listed on IDEAS
    23. repec:spr:sochwe:v:49:y:2017:i:1:d:10.1007_s00355-017-1056-6 is not listed on IDEAS

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