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Fairness and fairness for neighbors: the difference between the Myerson value and component-wise egalitarian solutions


  • Béal, Sylvain
  • Rémila, Eric
  • Solal, Philippe


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 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 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 players.

Suggested Citation

  • Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Fairness and fairness for neighbors: the difference between the Myerson value and component-wise egalitarian solutions," MPRA Paper 36857, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:36857

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    References listed on IDEAS

    1. Calvo, Emilio & Gutiérrez, Esther, 2010. "Solidarity in games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 196-203, November.
    2. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    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.
    4. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
    5. repec:wsi:igtrxx:v:11:y:2009:i:02:n:s0219198909002261 is not listed on IDEAS
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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. Sylvain Béal & André Casajus & Frank Huettner, 2015. "Efficient extensions of communication values," Working Papers hal-01376907, HAL.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

    More about this item


    Myerson value; component-wise egalitarian solutions; fairness; fairness for neighbors; two-step value;

    JEL classification:

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


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