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Linear efficient and symmetric values for TU-games: Sharing the joint gain of cooperation

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  • Chameni Nembua, C.

Abstract

Recently, Hermandez-Lamoneda et al. (2008) and independently Chameni and Andjiga (2008) gave an analytic formulation for all valued solutions to the n-person TU-games that satisfy linearity, efficiency and symmetry axioms. Our main purpose in this paper is to recast the proposed formulation to a more potentially interpretational one. We are focused on an interpretation based on the idea of marginal contribution, a concept already familiar in the Shapley value and the Solidarity value. A general null player axiom is introduced, and it turns out that any valued solution satisfying the three properties is characterized by a null player model.

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  • Chameni Nembua, C., 2012. "Linear efficient and symmetric values for TU-games: Sharing the joint gain of cooperation," Games and Economic Behavior, Elsevier, vol. 74(1), pages 431-433.
    • Handle: RePEc:eee:gamebe:v:74:y:2012:i:1:p:431-433
    DOI: 10.1016/j.geb.2011.07.003
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    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. 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. Francisco Sanchez-Sanchez & Ruben Juarez & Luis Hernandez-Lamoneda, 2008. "Solutions without dummy axiom for TU cooperative games," Economics Bulletin, AccessEcon, vol. 3(1), pages 1-9.
    4. Célestin Chameni Nembua & Nicolas Gabriel Andjiga, 2008. "Linear, efficient and symmetric values for TU-games," Economics Bulletin, AccessEcon, vol. 3(71), pages 1-10.
    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.
    6. repec:ebl:ecbull:v:3:y:2008:i:1:p:1-9 is not listed on IDEAS
    7. 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.
    8. repec:ebl:ecbull:v:3:y:2008:i:71:p:1-10 is not listed on IDEAS
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    Cited by:

    1. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Axioms of invariance for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 891-902, November.
    2. Casajus, André & Huettner, Frank, 2014. "On a class of solidarity values," European Journal of Operational Research, Elsevier, vol. 236(2), pages 583-591.
    3. 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.
    4. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "A Class of Solidarity Allocation Rules for TU-games," Working Papers 2015-03, CRESE.
    5. Casajus, André & Huettner, Frank, 2013. "Null players, solidarity, and the egalitarian Shapley values," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 58-61.
    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. 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.
    8. Radzik, Tadeusz, 2013. "Is the solidarity value close to the equal split value?," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 195-202.
    9. Chameni Nembua, C. & Miamo Wendji, C., 2016. "Ordinal equivalence of values, Pigou–Dalton transfers and inequality in TU-games," Games and Economic Behavior, Elsevier, vol. 99(C), pages 117-133.
    10. Lee, Joosung & Driessen, Theo S.H., 2012. "Sequentially two-leveled egalitarianism for TU games: Characterization and application," European Journal of Operational Research, Elsevier, vol. 220(3), pages 736-743.
    11. Maimo, Clovis Wendji, 2017. "Matrix representation of TU-games for Linear Efficient and Symmetric values," MPRA Paper 82416, University Library of Munich, Germany.
    12. Chameni Nembua, Célestin & Demsou, Themoi, 2013. "Ordinal equivalence of values and Pigou-Dalton transfers in TU-games," MPRA Paper 44895, University Library of Munich, Germany, revised 09 Mar 2013.
    13. Yokote, Koji & Kongo, Takumi & Funaki, Yukihiko, 2018. "The balanced contributions property for equal contributors," Games and Economic Behavior, Elsevier, vol. 108(C), pages 113-124.
    14. Emilio Calvo Ramón & Esther Gutiérrez-López, 2022. "The equal collective gains value in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 249-278, March.
    15. Nembua Célestin, Chameni & Wendji Clovis, Miamo, 2017. "On some decisive players for linear efficient and symmetric values in cooperative games with transferable utility," MPRA Paper 83670, University Library of Munich, Germany, revised 2017.

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    More about this item

    Keywords

    TU-games; Single valued solution; Shapley value; Marginal contribution; Null player axiom;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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