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Weighted component fairness for forest games

Listed author(s):
  • Béal, Sylvain
  • Rémila, Eric
  • Solal, Philippe

We study the set of allocation rules generated by component efficiency and weighted component fairness, a generalization of component fairness introduced by Herings et al. (2008). Firstly, if the underlying TU-game is superadditive, this set coincides with the core of a graph-restricted game associated with the forest game. Secondly, among this set, only the random tree solutions (Béal et al., 2010) induce Harsanyi payoff vectors for the associated graph-restricted game. We then obtain a new characterization of the random tree solutions in terms of component efficiency and weighted component fairness.

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File URL: http://www.sciencedirect.com/science/article/pii/S0165489612000261
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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 64 (2012)
Issue (Month): 2 ()
Pages: 144-151

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Handle: RePEc:eee:matsoc:v:64:y:2012:i:2:p:144-151
DOI: 10.1016/j.mathsocsci.2012.03.004
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. Richard Baron & Sylvain Béal & Philippe Solal & Éric Rémila, 2010. "Average Tree Solutions and the Distribution of Harsanyi Dividends," Post-Print halshs-00530610, HAL.
  2. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2010. "The average tree solution for cooperative games with communication structure," Other publications TiSEM 24359ac5-6399-42ee-8f0b-7, Tilburg University, School of Economics and Management.
  3. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," PSE - Labex "OSE-Ouvrir la Science Economique" hal-00803233, HAL.
  4. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
  5. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, vol. 203(2), pages 404-408, June.
  6. René van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute.
  7. Rene van den Brink & Gerard van der Laan & Nigel Moes, 2010. "Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities," Tinbergen Institute Discussion Papers 10-096/1, Tinbergen Institute.
  8. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2001. "The Myerson value for union stable structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 359-371, December.
  9. 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.
  10. René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(2), pages 349-364, November.
  11. Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.
  12. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
  13. Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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