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Social Networks

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Handbook of Dynamic Game Theory

Abstract

In this chapter, some applications of game theory in social network analysis are presented. We first focus on the opinion dynamics of a social network. Viewing the individuals as players of a game with appropriately defined action (opinion) sets and utility functions, we investigate the best response dynamics and its variants for the game, which would in effect represent the evolution of the individuals’ opinions within a social network. The action sets are defined according to the nature of the opinions, which may be continuous, as for the political beliefs of the individuals, or discrete, as for the type of technology adopted by the individuals to use in their daily lives. The utility functions, on the other hand, are to best capture the social behavior of the individuals such as conformity and stubbornness. For every formulation of the game, we characterize the formation of the opinions as time grows. In particular, we determine whether an agreement among all of the individuals is reached, a clustering of opinions occurs, or none of the said cases happens. We further investigate the Nash equilibria of the game and make clear if the game dynamics converges to one of the Nash equilibria. The rate of convergence to the equilibrium, if it is the case, is also obtained. We then turn our attention to decision-making processes (elections) in social networks, where a collective decision (social choice) must be made by multiple individuals (voters) with different preferences over the alternatives (candidates). We argue that the nonexistence of a perfectly fair social choice function that takes all voter preferences into account leads to the emergence of various strategic games in decision-making processes, most notably strategic voting, strategic candidacy, and coalition formation. While the strategic voting would be played among the voters, the other two games would be played among the candidates. We explicitly discuss the games of strategic candidacy and coalition formation.

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Notes

  1. 1.

    This definition of coordination games is specific to this chapter and may be different from other definitions used in the literature.

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Author information

Authors and Affiliations

  1. Coordinated Science Laboratory, University of Illinois, 61801, Urbana-Champaign, Urbana, IL, USA

    Sadegh Bolouki & Tamer Başar

  2. School of ECEE, Arizona State University, 85287, Tempe, AZ, USA

    Angelia Nedić

Authors
  1. Sadegh Bolouki
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  2. Angelia Nedić
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  3. Tamer Başar
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Corresponding author

Correspondence to Sadegh Bolouki .

Editor information

Editors and Affiliations

  1. Center for Advanced Study, University of Illinois Urbana-Champaign, Urbana, Illinois, USA

    Tamer Basar

  2. GERAD, HEC Montréal, Montreal, Québec, Canada

    Georges Zaccour

Section Editor information

  1. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1308 West Main, 61801, Urbana, IL, USA

    Tamer Başar

  2. Département de sciences de la décision, GERAD, HEC Montréal, Montreal, QC, Canada

    Georges Zaccour

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Bolouki, S., Nedić, A., Başar, T. (2017). Social Networks. In: Basar, T., Zaccour, G. (eds) Handbook of Dynamic Game Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-27335-8_32-1

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  • DOI: https://doi.org/10.1007/978-3-319-27335-8_32-1

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