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Measuring influence in command games

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  • Michel Grabisch

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Agnieszka Rusinowska

    ()
    (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)

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. For some influence functions we define the command games such that the influence functions are compatible with these games. We show that not for all influence functions such command games exist. Moreover, we propose a more general definition of the influence index and show that some power indices, which can be used in the command games, coincide with some expressions of the weighted influence indices. We show exact relations between an influence function and a follower function, between a command game and commandable players, and between influence functions and command games. An example of the Confucian model of society is broadly examined.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00269084.

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Date of creation: 2008
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Handle: RePEc:hal:cesptp:halshs-00269084

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Related research

Keywords: Banzhaf index ; Coleman indices ; command game ; follower of a coalition ; influence function ; influence indices ; Shapley-Shubik index;

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References

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  1. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(1), pages 132-152, October.
  2. Michel Grabisch & Agnieszka Rusinowska, 2008. "A model of influence in a social network," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne b08066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. repec:hal:journl:halshs-00260863 is not listed on IDEAS
  4. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence among players with an ordered set of possible actions," Working Papers, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure 0801, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  5. M. Albizuri & Jesus Aurrekoetxea, 2006. "Coalition Configurations and the Banzhaf Index," Social Choice and Welfare, Springer, Springer, vol. 26(3), pages 571-596, June.
  6. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(1), pages 153-170, October.
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Cited by:
  1. Tomas Rodriguez Barraquer, 2013. "From sets of equilibria to structures of interaction underlying binary games of strategic complements," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp655, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. 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.
  3. Michel Grabisch & Agnieszka Rusinowska, 2013. "A Model of Influence Based on Aggregation Function," PSE - Labex "OSE-Ouvrir la Science Economique", HAL halshs-00906367, 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, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 11058, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  5. Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2011. "A study of the dynamic of influence through differential equations," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 11022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  6. Michel Grabisch & Agnieszka Rusinowska, 2008. "Influence functions, followers and command games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00355632, HAL.
  7. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, Springer, vol. 69(4), pages 635-656, October.
  8. Robin, Stéphane & Rusinowska, Agnieszka & Villeval, Marie Claire, 2014. "Ingratiation: Experimental evidence," European Economic Review, Elsevier, Elsevier, vol. 66(C), pages 16-38.
  9. Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2012. "A study of the dynamic of influence through differential equations," PSE - Labex "OSE-Ouvrir la Science Economique", HAL halshs-00699012, HAL.
  10. 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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