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Strategic influence in social networks

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Abstract

We consider a model of influence with a set of non-strategic agents and two strategic agents. The non-strategic 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 opinions, 1 and 0 respectively, and are characterized by the magnitude of the impact they can exert on non-strategic agents. Each strategic agent forms a link with one non-strategic agent in order to alter the average opinion that eventually emerges 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 non-strategic agents. We focus on the existence and the characterization of equilibria in pure strategy in this setting. Simple examples show that the existence of a pure strategy equilibrium does depend on the structure of the network. The characterization of equilibrium we obtain emphasizes on the one hand the influenceability of target agents and on the other hand their centrality whose natural measure in our context defines a new concept, related to betweenness centrality, that we call intermediacy. We also show that in the case where the two strategic agents have the same impact, symmetric equilibria emerge as natural solutions whereas in the case where the impacts are uneven, the strategic players generally have differentiated equilibrium targets, the high-impacts agent focusing on centrality and the low-impact agent on influenceability

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  • Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska & Emily Tanimura, 2015. "Strategic influence in social networks," Documents de travail du Centre d'Economie de la Sorbonne 15006, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:15006
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    Cited by:

    1. Antoine Mandel & Xavier Venel, 2022. "Sequential competition and the strategic origins of preferential attachment," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 483-508, November.
    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, 2017. "Dynamic competition over social networks Dynamic competition over social networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01524453, HAL.
    4. Mandel, Antoine & Venel, Xavier, 2020. "Dynamic competition over social networks," European Journal of Operational Research, Elsevier, vol. 280(2), pages 597-608.
    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. Tsakas, Nikolas, 2017. "Diffusion by imitation: The importance of targeting agents," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 118-151.
    7. Akylai Taalaibekova, 2018. "Opinion formation in social networks," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(2), pages 85-108.
    8. 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".
    9. Venel, Xavier, 2021. "Regularity of dynamic opinion games," Games and Economic Behavior, Elsevier, vol. 126(C), pages 305-334.
    10. Antoine Mandel & Xavier Venel, 2017. "Dynamic competition over social networks Dynamic competition over social networks," Post-Print halshs-01524453, HAL.
    11. 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.
    12. Tsakas, Nikolas, 2024. "Optimal influence under observational learning," Mathematical Social Sciences, Elsevier, vol. 128(C), pages 41-51.

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    More about this item

    Keywords

    Influence networks; beliefs; DeGroot model; strategic player; convergence; consensus; equilibrium;
    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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