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Different Approaches to Influence Based on Social Networks and Simple Games

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  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Agnieszka Rusinowska

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We present an overview of research on a certain model of influence in a social network. Each agent has to make an acceptance/rejection decision, and he has an inclination to choose either the yes-action or the no-action. The agents are embedded in a social network which models influence between them. Due to the influence, a decision of an agent may differ from his preliminary inclination. Such a transformation between the agents' inclinations and their decisions are represented by an influence function. Follower functions encode the players who constantly follow the opinion of a given unanimous coalition. We examine properties of the influence and follower functions and study the relation between them. The model of influence is also compared to the framework of command games in which a simple game is built for each agent. We study the relation between command games and influence functions. We also define influence indices and determine the relations between these indices and some well-known power indices. Furthermore, we enlarge the set of possible yes/no actions to multi-choice games and investigate the analogous tools related to influence in the multi-choice model.

Suggested Citation

  • Michel Grabisch & Agnieszka Rusinowska, 2010. "Different Approaches to Influence Based on Social Networks and Simple Games," Post-Print hal-00514850, HAL.
    • Handle: RePEc:hal:journl:hal-00514850
    DOI: 10.1007/978-3-642-02865-6_13
    Note: View the original document on HAL open archive server: https://hal.science/hal-00514850
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    1. Annick Laruelle & Federico Valenciano, 2005. "Assessing success and decisiveness in voting situations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 171-197, January.
    2. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
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    5. Michel Grabisch & Agnieszka Rusinowska, 2009. "Measuring influence in command games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 177-209, August.
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    1. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    2. 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.
    3. 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.
    4. Maurice Koster & Sascha Kurz & Ines Lindner & Stefan Napel, 2017. "The prediction value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 433-460, February.
    5. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    6. 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.

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