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Dynamic competition over social networks Dynamic competition over social networks

Author

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  • Antoine Mandel

    (PSE - Paris School of Economics, CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne)

  • Xavier Venel

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

Abstract

We provide an analytical approach to the problem of influence maximization in a social network when two players compete by means of dynamic targeting strategies. We formulate the problem as a two-player zero-sum stochastic game. We prove the existence of the uniform value: if the players are sufficiently patient, both players can guarantee the same mean-average opinion without knowing the exact discount factor. Further, we put forward some elements for the characterization of equilibrium strategies. In general, players must implement a trade-off between a forward-looking perspective, according to which they shall aim at maximizing the future spread of their opinion in the network, and a backward-looking perspective, according to which they shall aim at counteracting their opponent's previous actions. When the influence potential of players is small, an equilibrium strategy is to systematically target the agent with the largest eigenvector centrality.

Suggested Citation

  • 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.
  • Handle: RePEc:hal:cesptp:halshs-01524453
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01524453
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    References listed on IDEAS

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    1. Enriqueta Aragonès & Micael Castanheira & Marco Giani, 2012. "Electoral Competition through Issue Selection," UFAE and IAE Working Papers 903.12, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
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    3. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2000. "Blackwell Optimality in Markov Decision Processes with Partial Observation," Discussion Papers 1292, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    5. Daron Acemoğlu & Giacomo Como & Fabio Fagnani & Asuman Ozdaglar, 2013. "Opinion Fluctuations and Disagreement in Social Networks," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 1-27, February.
    6. Pradeep Dubey & Rahul Garg & Bernard De Meyer, 2006. "Competing for Customers in a Social Network," Cowles Foundation Discussion Papers 1591, Cowles Foundation for Research in Economics, Yale University.
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    10. Jérôme Renault, 2012. "The Value of Repeated Games with an Informed Controller," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 154-179, February.
    11. Pablo Amorós & M. Puy, 2013. "Issue convergence or issue divergence in a political campaign?," Public Choice, Springer, vol. 155(3), pages 355-371, June.
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    13. Xavier Venel, 2015. "Commutative Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 403-428, February.
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    More about this item

    Keywords

    Stochastic games; Social network; Dynamic games; Targeting; Jeux stochastiques; Jeux dynamiques; Réseaux sociaux;

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