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Fairness and Fairness for Neighbors: The Difference between the Myerson Value and Component-Wise Egalitarian Solutions

Author

Listed:
  • Sylvain Béal

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Éric Rémila

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, LIP - Laboratoire de l'Informatique du Parallélisme - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - Inria - Institut National de Recherche en Informatique et en Automatique - Université de Lyon - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Solal

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We replace the axiom of fairness used in the characterization of the Myerson value (Myerson, 1977) by fairness for neighbors in order to characterize the component-wise egalitarian solution. When a link is broken, fairness states that the two players incident to the link should be affected similarly while fairness for neighbors states that a player incident to the link and any of his other neighbors should be affected similarly. Fairness for neighbors is also used to characterize the component-wise egalitarian surplus solution and a two-step egalitarian surplus solution. These results highlight that egalitarian and marginalistic allocation rules can be obtained by applying the same equal gain/loss property to different types of player

Suggested Citation

  • Sylvain Béal & Éric Rémila & Philippe Solal, 2012. "Fairness and Fairness for Neighbors: The Difference between the Myerson Value and Component-Wise Egalitarian Solutions," Post-Print halshs-00699641, HAL.
    • Handle: RePEc:hal:journl:halshs-00699641
    DOI: 10.1016/j.econlet.2012.05.020
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    Cited by:

    1. Guang Zhang & Erfang Shan & Liying Kang & Yanxia Dong, 2017. "Two efficient values of cooperative games with graph structure based on $$\tau $$ τ -values," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 462-482, August.
    2. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
    3. Sylvain Béal & André Casajus & Frank Huettner, 2018. "Efficient extensions of communication values," Annals of Operations Research, Springer, vol. 264(1), pages 41-56, May.
    4. Daniel Li Li & Erfang Shan, 2017. "Cost sharing on prices for games on graphs," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 676-688, October.
    5. Sylvain Béal & André Casajus & Frank Huettner, 2015. "Efficient extensions of the Myerson value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 819-827, December.
    6. Casajus, André & Huettner, Frank, 2014. "Null, nullifying, or dummifying players: The difference between the Shapley value, the equal division value, and the equal surplus division value," Economics Letters, Elsevier, vol. 122(2), pages 167-169.
    7. Shan, Erfang & Zhang, Guang & Dong, Yanxia, 2016. "Component-wise proportional solutions for communication graph games," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 22-28.
    8. Béal, Sylvain & Casajus, André & Huettner, Frank, 2016. "On the existence of efficient and fair extensions of communication values for connected graphs," Economics Letters, Elsevier, vol. 146(C), pages 103-106.
    9. Shi, Jilei & Shan, Erfang, 2020. "Weighted component-wise solutions for graph games," Economics Letters, Elsevier, vol. 192(C).
    10. Erfang Shan & Zhiqiang Yu & Wenrong Lyu, 2023. "Union-wise egalitarian solutions in cooperative games with a coalition structure," 4OR, Springer, vol. 21(3), pages 533-545, September.
    11. van den Brink, René & Khmelnitskaya, Anna & van der Laan, Gerard, 2012. "An efficient and fair solution for communication graph games," Economics Letters, Elsevier, vol. 117(3), pages 786-789.
    12. Daniel Li & Erfang Shan, 2025. "Solidarity Value for Graph Games," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-13, August.
    13. 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.
    14. 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.
    15. 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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    JEL classification:

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

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