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On some decisive players for linear efficient and symmetric values in cooperative games with transferable utility

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  • Nembua Célestin, Chameni
  • Wendji Clovis, Miamo

Abstract

The main goal of the paper is to shed light on economic allocations issues, in particular by focusing on individuals who receive nothing (that is an amount of zero allocation or payoff). It is worth noting that such individuals may be considered, in some contexts, as poor or socially excluded. To this end, our study relies on the notion of cooperative games with transferable utility and the Linear Efficient and Symmetric values (called LES values) are considered as allocation rules. Null players in Shapley sense are extensively studied ; two broader classes of null players are introduced. The analysis is facilitated by the help of a parametric representation of LES values. It is clearly shown that the control of what a LES value assigns as payoffs to null players gives significant information about the characterization of the value. Several axiomatic characterizations of subclasses of LES values are provided using our approach.

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:83670
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    References listed on IDEAS

    as
    1. 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.
    2. Célestin Chameni Nembua & Nicolas Gabriel Andjiga, 2008. "Linear, efficient and symmetric values for TU-games," Economics Bulletin, AccessEcon, vol. 3(71), pages 1-10.
    3. 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.
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    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    11. 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.
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    More about this item

    Keywords

    TU-game; Linear Efficient and Symmetric value; Null players; Average null players; Shapley value; Solidarity value.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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