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Measuring influence in command games

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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.

Suggested Citation

  • Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence in command games," Documents de travail du Centre d'Economie de la Sorbonne b08078, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:b08078
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2008/B08078.pdf
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    References listed on IDEAS

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    1. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
    2. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
    3. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
    4. Michel Grabisch & Agnieszka Rusinowska, 2008. "Measuring influence among players with an ordered set of possible actions," Working Papers 0801, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    5. Michel Grabisch & Agnieszka Rusinowska, 2007. "Influence Indices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00142479, HAL.
      • Agnieszka Rusinowska & Michel Grabisch, 2007. "Influence Indices," Working Papers 0705, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    6. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    7. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
    8. M. Albizuri & Jesus Aurrekoetxea, 2006. "Coalition Configurations and the Banzhaf Index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 571-596, June.
    9. R J Johnston, 1978. "On the measurement of power: some reactions to Laver," Environment and Planning A, Pion Ltd, London, vol. 10(8), pages 907-914, August.
    10. repec:hal:journl:halshs-00142479 is not listed on IDEAS
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    Cited by:

    1. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.
    2. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    3. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    4. 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 11022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Robin, Stéphane & Rusinowska, Agnieszka & Villeval, Marie Claire, 2014. "Ingratiation: Experimental evidence," European Economic Review, Elsevier, vol. 66(C), pages 16-38.
    6. repec:hal:journl:hal-00633859 is not listed on IDEAS
    7. Tomas Rodriguez Barraquer, 2013. "From sets of equilibria to structures of interaction underlying binary games of strategic complements," Discussion Paper Series dp655, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    8. Michel Grabisch & Agnieszka Rusinowska, 2010. "Iterating influence between players in a social network," Documents de travail du Centre d'Economie de la Sorbonne 10089, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. repec:hal:journl:halshs-00543840 is not listed on IDEAS
    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.

    More about this item

    Keywords

    Influence function; follower; influence index; command game; commandable player; Shapley-Shubik index; Banzhaf index; Coleman indicies; König-Bräuninger index.;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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