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Influence functions, followers and command games

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  • Michel Grabisch

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

  • Agnieszka Rusinowska

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

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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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00583867.

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Date of creation: May 2011
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Publication status: Published, Games and Economic Behavior, 2011, 72, 1, 123-138
Handle: RePEc:hal:cesptp:halshs-00583867

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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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Citations

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Cited by:
  1. Michel Grabisch & Agnieszka Rusinowska, 2011. "A model of influence based on aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00639677, HAL.
  2. Büchel, Berno & Hellmann, Tim & Klößner, Stefan, 2013. "Opinion Dynamics and Wisdom under Conformity," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79770, Verein für Socialpolitik / German Economic Association.
  3. FÖRSTER, Manuel & GRABISCH, Michel & RUSINOWSKA, Agnieszka, 2013. "Anonymous social influence," CORE Discussion Papers 2013028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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. 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.
  6. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, Open Access Journal, vol. 2(1), pages 45-77, March.
  7. 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.

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