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Influence functions, followers and command games

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  • Michel Grabisch

    ()
    (Centre d'Economie de la Sorbonne)

  • Agnieszka Rusinowska

    ()
    (GATE)

Abstract

We study and compare two frameworks : a model of influence, and command games. In the influence model, in which players are to make a certain acceptance/rejection decision, due to influence of other players, the decision of a player may be different from his inclination. We study a relation between two central concepts of this model : influence function, and follower function. We deliver sufficient and necessary conditions for a function to be a follower function, and we describe the structure of the set of all influence functions that lead to a given follower function. In the command structure introduced by Hu and Shapley, for each player a simple game called the command game is built. One of the central concepts of this model is the concept of command function. We deliver sufficient and necessary conditions for a function to be a command function, and describe the minimal sets generating a normal command game. We also study the relation between command games and influence functions. A sufficient and necessary condition for the equivalence between an influence function and a normal command game is delivered.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2008/B08080.pdf
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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number b08080.

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Length: 24 pages
Date of creation: Dec 2008
Date of revision:
Handle: RePEc:mse:cesdoc:b08080

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Keywords: Influence function; follower function; lower and upper inverses; kernel; command game; command function; minimal sets generating a command game.;

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References

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  17. 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.
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Citations

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Cited by:
  1. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
  2. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, Open Access Journal, vol. 2(1), pages 45-77, March.
  3. Tomas Rodriguez Barraquer, 2013. "From sets of equilibria to structures of interaction underlying binary games of strategic complements," Discussion Paper Series dp655, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. Berno Buechel & Tim Hellmann & Stefan Kölßner, 2014. "Opinion Dynamics and Wisdom under Conformity," Working Papers 2014.51, Fondazione Eni Enrico Mattei.
  5. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
  6. Emmanuel Maruani & Michel Grabisch & Agnieszka Rusinowska, 2012. "A study of the dynamic of influence through differential equations," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00699012, HAL.
  7. 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.
  8. repec:hal:cesptp:halshs-00587820 is not listed on IDEAS

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