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Measuring influence in command games

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  • Michel Grabisch

    ()

  • Agnieszka Rusinowska

    ()

Abstract

In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions are compatible with the command games, in the sense that each commandable player for a coalition in the command game is a follower of the coalition under the command influence function. Some of the presented influence functions are equivalent to the command games, that is, they are compatible with the command games, and additionally each follower of a coalition under the command influence function is also a commandable player for that coalition in the command games. For some influence functions, we define the equivalent command games. We show that not for all influence functions the compatible command games exist. Moreover, we propose a more general definition of the influence index and show that under some assumptions, some power indices, which can be used in the command games, coincide with some expressions of the weighted influence indices. Both the Shapley-Shubik index and the Banzhaf index are equal to a difference between the weighted influence indices under some influence functions, and the only difference between thes two power indices lies in the weights for the influence indices. An example of the Confucian model od society is broadly examined.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s00355-008-0350-8
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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 33 (2009)
Issue (Month): 2 (August)
Pages: 177-209

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Handle: RePEc:spr:sochwe:v:33:y:2009:i:2:p:177-209

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References

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  1. Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Documents de travail du Centre d'Economie de la Sorbonne b08066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
  3. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence among players with an ordered set of possible actions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00260863, HAL.
  4. M. Albizuri & Jesus Aurrekoetxea, 2006. "Coalition Configurations and the Banzhaf Index," Social Choice and Welfare, Springer, vol. 26(3), pages 571-596, June.
  5. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
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Citations

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Cited by:
  1. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Documents de travail du Centre d'Economie de la Sorbonne b08080, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Agnieszka Rusinowska & Michel Grabisch, 2010. "A model of influence with an ordered set of possible actions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00519413, HAL.
  3. Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2011. "A study of the dynamic of influence through differential equations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00587820, HAL.
  4. Michel Grabisch & Agnieszka Rusinowska, 2011. "A model of influence based on aggregation functions," Documents de travail du Centre d'Economie de la Sorbonne 11058, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  5. Michel Grabisch & Agnieszka Rusinowska, 2010. "Iterating influence between players in a social network," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00543840, HAL.
  6. Agnieszka Rusinowska & Rudolf Berghammer & Harrie De Swart & Michel Grabisch, 2011. "Social networks: Prestige, centrality, and influence (Invited paper)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633859, HAL.

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