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Balanced per capita contributions and level structure of cooperation

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  • María Gómez-Rúa
  • Juan Vidal-Puga

Abstract

We define a new value for games with levels structure. We introduce a new property in this class of games, balanced per capita contributions, which is related with others in the literature. We provide an axiomatic characterization of this value using this new property.
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  • María Gómez-Rúa & Juan Vidal-Puga, 2011. "Balanced per capita contributions and level structure of cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 167-176, July.
    • Handle: RePEc:spr:topjnl:v:19:y:2011:i:1:p:167-176
    DOI: 10.1007/s11750-009-0122-3
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    References listed on IDEAS

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    2. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    3. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2005. "The component fairness solution for cycle-free graph games," Research Memorandum 057, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    5. E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 1-9.
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    7. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    8. Gérard Hamiache, 2006. "A value for games with coalition structures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 93-105, January.
    9. Sanchez S., Francisco, 1997. "Balanced Contributions Axiom in the Solution of Cooperative Games," Games and Economic Behavior, Elsevier, vol. 20(2), pages 161-168, August.
    10. Calvo, Emilio & Javier Lasaga, J. & Winter, Eyal, 1996. "The principle of balanced contributions and hierarchies of cooperation," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 171-182, June.
    11. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    12. Levy, Anat & Mclean, Richard P., 1989. "Weighted coalition structure values," Games and Economic Behavior, Elsevier, vol. 1(3), pages 234-249, September.
    13. Juan Vidal-Puga, 2005. "Implementation of the Levels Structure Value," Annals of Operations Research, Springer, vol. 137(1), pages 191-209, July.
    14. Vidal-Puga, Juan, 2012. "The Harsanyi paradox and the “right to talk” in bargaining among coalitions," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 214-224.
    15. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 227-240.
    16. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    17. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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    Citations

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    Cited by:

    1. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    2. Manfred Besner, 2022. "Harsanyi support levels solutions," Theory and Decision, Springer, vol. 93(1), pages 105-130, July.
    3. René Brink & Anna Khmelnitskaya & Gerard Laan, 2016. "An Owen-type value for games with two-level communication structure," Annals of Operations Research, Springer, vol. 243(1), pages 179-198, August.
    4. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    5. Besner, Manfred, 2018. "The weighted Shapley support levels values," MPRA Paper 87617, University Library of Munich, Germany.
    6. Jilei Shi & Lei Cai & Erfang Shan & Wenrong Lyu, 2022. "A value for cooperative games with coalition and probabilistic graph structures," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 646-671, April.
    7. Besner, Manfred, 2018. "Proportional Shapley levels values," MPRA Paper 87120, University Library of Munich, Germany.
    8. Vidal-Puga, Juan, 2012. "The Harsanyi paradox and the “right to talk” in bargaining among coalitions," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 214-224.
    9. Xun-Feng Hu & Gen-Jiu Xu & Deng-Feng Li, 2019. "The Egalitarian Efficient Extension of the Aumann–Drèze Value," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1033-1052, June.
    10. F. Fernández & J. Puerto, 2012. "The minimum cost shortest-path tree game," Annals of Operations Research, Springer, vol. 199(1), pages 23-32, October.
    11. Besner, Manfred, 2020. "Values for level structures with polynomial-time algorithms, relevant coalition functions, and general considerations," MPRA Paper 99355, University Library of Munich, Germany.
    12. 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.
    13. Besner, Manfred, 2018. "Two classes of weighted values for coalition structures with extensions to level structures," MPRA Paper 87742, University Library of Munich, Germany.
    14. Xun-Feng Hu & Deng-Feng Li, 2021. "The Equal Surplus Division Value for Cooperative Games with a Level Structure," Group Decision and Negotiation, Springer, vol. 30(6), pages 1315-1341, December.
    15. Besner, Manfred, 2018. "Weighted Shapley hierarchy levels values," MPRA Paper 88160, University Library of Munich, Germany.
    16. Besner, Manfred, 2023. "The per capita Shapley support levels value," MPRA Paper 116457, University Library of Munich, Germany.
    17. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    18. Hu, Xun-Feng & Li, Deng-Feng & Xu, Gen-Jiu, 2018. "Fair distribution of surplus and efficient extensions of the Myerson value," Economics Letters, Elsevier, vol. 165(C), pages 1-5.

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    More about this item

    Keywords

    Level structure; Value; Balanced per capita contributions; 91A06; 91A12;
    All these keywords.

    JEL classification:

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

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