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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 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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File URL: http://www.sciencedirect.com/science/article/pii/S0165176512002881
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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
Contact details of provider: Web page: http://www.elsevier.com/locate/ecolet

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  1. repec:dgr:uvatin:2011052 is not listed on IDEAS
  2. 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.
  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. repec:dgr:uvatin:20110052 is not listed on IDEAS
  5. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
  6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  7. Emilio Calvo & Maria Esther Gutierrez, 2010. "Solidarity in games with a coalition structure," Discussion Papers in Economic Behaviour 0810, University of Valencia, ERI-CES.
  8. 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.
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