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Strategic Influence in Social Networks

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  • Michel Grabisch

    () (Paris School of Economics, Université Paris I Panthéon-Sorbonne, Centre d’Economie de la Sorbonne, 75647 Paris Cedex 13, France)

  • Antoine Mandel

    () (Paris School of Economics, Université Paris I Panthéon-Sorbonne, Centre d’Economie de la Sorbonne, 75647 Paris Cedex 13, France)

  • Agnieszka Rusinowska

    () (Paris School of Economics—CNRS, Université Paris I Panthéon-Sorbonne, Centre d’Economie de la Sorbonne, 75647 Paris Cedex 13, France)

  • Emily Tanimura

    () (Université Paris I Panthéon-Sorbonne, Centre d’Economie de la Sorbonne, 75647, Paris Cedex 13, France)

Abstract

We consider a model of influence with a set of nonstrategic agents and two strategic agents. The nonstrategic agents have initial opinions and are linked through a simply connected network. They update their opinions as in the DeGroot model. The two strategic agents have fixed and opposed opinions. They each form a link with a nonstrategic agent in order to influence the average opinion that emerges due to interactions in the network. This procedure defines a zero-sum game whose players are the two strategic agents and whose strategy set is the set of nonstrategic agents. We focus on the existence and the characterization of pure strategy equilibria in this setting. Simple examples show that the existence of a pure strategy equilibrium does depend on the structure of the network. We characterize equilibrium with two notions: the influenceability of target agents, and their centrality, which in our context we call “intermediacy.” We also show that when the two strategic agents have the same impact, symmetric equilibria emerge as natural solutions. In the case where the impacts are uneven, the game has only equilibria in mixed strategies, the high impact agent focuses on his own centrality/intermediacy and the influenceability of his opponent’s target while the low influence agent focuses on the influenceability of his own target.

Suggested Citation

  • Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska & Emily Tanimura, 2018. "Strategic Influence in Social Networks," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 29-50, February.
  • Handle: RePEc:inm:ormoor:v:43:y:2018:i:1:p:29-50
    DOI: 10.1287/moor.2017.0853
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    References listed on IDEAS

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    Cited by:

    1. Tsakas, Nikolas, 2017. "Diffusion by imitation: The importance of targeting agents," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 118-151.
    2. Grabisch, Michel & Poindron, Alexis & Rusinowska, Agnieszka, 2019. "A model of anonymous influence with anti-conformist agents," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    3. Antoine Mandel & Xavier Venel, 2018. "Sequential competition and the strategic origins of preferential attachment," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01960682, HAL.
    4. Tabasso, Nicole, 2019. "Diffusion of multiple information: On information resilience and the power of segregation," Games and Economic Behavior, Elsevier, vol. 118(C), pages 219-240.
    5. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    6. Sebastiano Della Lena, 2019. "Non-Bayesian Social Learning and the Spread of Misinformation in Networks," Working Papers 2019:09, Department of Economics, University of Venice "Ca' Foscari".
    7. Mandel, Antoine & Venel, Xavier, 2020. "Dynamic competition over social networks," European Journal of Operational Research, Elsevier, vol. 280(2), pages 597-608.
    8. Antoine Mandel & Xavier Venel, 2017. "Dynamic competition over social networks Dynamic competition over social networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01524453, HAL.
    9. Antoine Mandel & Xavier Venel, 2017. "Dynamic competition over social networks Dynamic competition over social networks," Post-Print halshs-01524453, HAL.
    10. Akylai Taalaibekova, 2018. "Opinion formation in social networks," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 2, pages 85-108.

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    More about this item

    Keywords

    networks; influence; centrality; strategic agents; targeting; lobbying;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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