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Monotonicity of power in weighted voting games with restricted communication

  • Napel, Stefan
  • Nohn, Andreas
  • Alonso-Meijide, José Maria

Indices that evaluate the distribution of power in simple games are commonly required to be monotonic in voting weights when the game represents a voting body such as a shareholder meeting, parliament, etc. The standard notions of local or global monotonicity are bound to be violated, however, if cooperation is restricted to coalitions that are connected by a communication graph. This paper proposes new monotonicity concepts for power in games with communication structure and investigates the monotonicity properties of the Myerson value, the restricted Banzhaf value, the position value, and the average tree solution.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 64 (2012)
Issue (Month): 3 ()
Pages: 247-257

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Handle: RePEc:eee:matsoc:v:64:y:2012:i:3:p:247-257
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Yang, Z., 2010. "The average tree solution for cooperative games with communication structure," Games and Economic Behavior, Elsevier, vol. 68(2), pages 626-633, March.
  2. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting Power in the EU Council of Ministers and Fair Decision Making in Distributive Politics," IDEI Working Papers 716, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. 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.
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  5. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2009. "Average tree solutions and the distribution of Harsanyi dividends," MPRA Paper 17909, University Library of Munich, Germany.
  6. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer, vol. 40(1), pages 87-110, February.
  7. Manfred J. Holler & Stefan Napel, 2004. "Monotonicity of power and power measures," Theory and Decision, Springer, vol. 56(2_2), pages 93-111, 02.
  8. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
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  10. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
  11. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
  12. Gérard Hamiache, 2011. "Graph monotonic values," Social Choice and Welfare, Springer, vol. 37(2), pages 287-307, July.
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  14. Takumi Kongo, 2010. "Difference between the position value and the Myerson value is due to the existence of coalition structures," International Journal of Game Theory, Springer, vol. 39(4), pages 669-675, October.
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  18. J. Alonso-Meijide & C. Bowles & M. Holler & S. Napel, 2009. "Monotonicity of power in games with a priori unions," Theory and Decision, Springer, vol. 66(1), pages 17-37, January.
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  20. Marco Slikker, 2005. "Link Monotonic Allocation Schemes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 473-489.
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