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

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

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 players.

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Bibliographic Info

Article provided by Elsevier in its journal Economics Letters.

Volume (Year): 117 (2012)
Issue (Month): 1 ()
Pages: 263-267

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Handle: RePEc:eee:ecolet:v:117:y:2012:i:1:p:263-267

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Related research

Keywords: Myerson value; Component-wise egalitarian solutions; Fairness; Fairness for neighbors; Two-step value;

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References

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  1. Rene van den Brink & Anna Khmelnitskaya & Gerard van der Laan, 2011. "An Efficient and Fair Solution for Communication Graph Games," Tinbergen Institute Discussion Papers 11-052/1, Tinbergen Institute.
  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. Calvo, Emilio & Gutiérrez, Esther, 2010. "Solidarity in games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 196-203, November.
  6. Yoshio Kamijo, 2009. "A Two-Step Shapley Value For Cooperative Games With Coalition Structures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 207-214.
  7. repec:dgr:uvatin:2011052 is not listed on IDEAS
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Cited by:
  1. 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.
  2. 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.

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