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Dynamic competition over social networks

Author

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  • Mandel, Antoine
  • Venel, Xavier

Abstract

We propose an analytical approach to the problem of influence maximization in a social network where 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 can guarantee the same mean-average opinion without knowing the exact length of the game. Furthermore, 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 aim to maximize the future spread of their opinion in the network, and a backward-looking perspective, according to which they aim to counteract their opponent’s previous actions. When the influence potential of players is small, we describe an equilibrium through a one-shot game based on eigenvector centrality.

Suggested Citation

  • Mandel, Antoine & Venel, Xavier, 2020. "Dynamic competition over social networks," European Journal of Operational Research, Elsevier, vol. 280(2), pages 597-608.
    • Handle: RePEc:eee:ejores:v:280:y:2020:i:2:p:597-608
    DOI: 10.1016/j.ejor.2019.07.028
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    Cited by:

    1. Juli'an Chitiva & Xavier Venel, 2024. "Continuous Social Networks," Papers 2407.11710, arXiv.org, revised Jan 2025.
    2. de Vos, Wout & Borm, Peter & Hamers, Herbert, 2025. "A Game of Influence on Opinion Formation - Precision Targeting in the Modern Information Space," Discussion Paper 2025-005, Tilburg University, Center for Economic Research.
    3. de Vos, Wout & Borm, Peter & Hamers, Herbert, 2025. "A Game of Influence on Opinion Formation - Precision Targeting in the Modern Information Space," Other publications TiSEM b21371ea-a12a-4e8d-8b21-f, Tilburg University, School of Economics and Management.
    4. Liu, Yezheng & Qian, Yang & Jiang, Yuanchun & Shang, Jennifer, 2020. "Using favorite data to analyze asymmetric competition: Machine learning models," European Journal of Operational Research, Elsevier, vol. 287(2), pages 600-615.
    5. Carayannis, Elias G. & Grigoroudis, Evangelos & Wurth, Bernd, 2022. "OR for entrepreneurial ecosystems: A problem-oriented review and agenda," European Journal of Operational Research, Elsevier, vol. 300(3), pages 791-808.
    6. Emilien Macault, 2022. "Stochastic Consensus and the Shadow of Doubt," Papers 2201.12100, arXiv.org.
    7. Cao, Yiyin & Dang, Chuangyin & Xiao, Zhongdong, 2022. "A differentiable path-following method to compute subgame perfect equilibria in stationary strategies in robust stochastic games and its applications," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1032-1050.
    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. Aihua Lin & Yukun Xu & Huafu Shen, 2023. "Quantitative Analysis of Human Behavior in Environmental Protection," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 14(3), pages 2982-3009, September.
    10. Tavasoli, Ali & Shakeri, Heman & Ardjmand, Ehsan & Young, William A., 2021. "Incentive rate determination in viral marketing," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1169-1187.
    11. Mishra, Rajat & Rasheed, Abdul A. & Yasar, Mahmut & Napier, Randy & Nakkas, Alper, 2021. "Inventory positions in US manufacturing: A competitive dynamics approach," International Journal of Production Economics, Elsevier, vol. 238(C).
    12. Della Lena, Sebastiano, 2024. "The spread of misinformation in networks with individual and social learning," European Economic Review, Elsevier, vol. 168(C).
    13. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.

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    Keywords

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    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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