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Influence functions, followers and command games

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  • Grabisch, Michel
  • Rusinowska, Agnieszka

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.

Suggested Citation

  • Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
  • Handle: RePEc:eee:gamebe:v:72:y:2011:i:1:p:123-138
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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. 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.
    4. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    5. Förster, Manuel & Grabisch, Michel & Rusinowska, Agnieszka, 2013. "Anonymous social influence," Games and Economic Behavior, Elsevier, vol. 82(C), pages 621-635.
    6. 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.
    7. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, Open Access Journal, vol. 2(1), pages 1-33, March.
    8. Dominik Karos, 2016. "Coordinated Adoption of Social Innovations," Economics Series Working Papers 797, University of Oxford, Department of Economics.
    9. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01659148, HAL.
    10. Ulrich Faigle & Michel Grabisch, 2017. "Game Theoretic Interaction and Decision: A Quantum Analysis," Documents de travail du Centre d'Economie de la Sorbonne 17046, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    11. Karos, Dominik & Peters, Hans, 2015. "Indirect control and power in mutual control structures," Games and Economic Behavior, Elsevier, vol. 92(C), pages 150-165.
    12. repec:gam:jgames:v:8:y:2017:i:4:p:48-:d:117821 is not listed on IDEAS
    13. 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 function Lower and upper inverses Kernel Command game Command function Minimal sets generating a command game;

    JEL classification:

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

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