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Optimal Influence Strategies in Social Networks

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Abstract

This paper suggests a modeling framework to investigate the optimal strategy followed by a monopolistic firm aiming to manipulate the process of opinion formation in a social network. The monopolist and a set of consumers communicate to form their beliefs about the underlying product quality. Since the firm’s associated optimization problem can be analytically solved only under specific assumptions, we rely on the sequential quadratic programming computational approach to characterize the equilibrium. When consumers’ initial beliefs are uniform, the firm’s optimal influence strategy always involves targeting the most influential consumer. For the case of non-uniform initial beliefs, the monopolist might target the less influential consumer if the latter’s initial opinion is low enough. The probability of investing more in the consumer with the lower influence increases with the distance between consumers’ initial beliefs and with the degree of trust attributed on consumers by the firm. The firm’s profit is minimized when consumers’ influences become equal, implying that the firm benefits from the presence of consumers with divergent strategic locations in the network. In the absence of a binding constraint on total investment, the monopolist’s incentives to manipulate the network decrease with consumers’ initial beliefs and might either increase or decrease with the trust put in consumers’ opinion by the firm. Finally, the firm’s strategic motivation to communicate persistently high beliefs during the opinion formation process is positively associated with the market size, with the available budget and with the direct influence of the most influential consumer on the other but negatively associated with consumers’ initial valuation of the good.

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Notes

  1. In a similar spirit, Coleman (1988, 2000) has stressed the importance of closure as a structural property of social networks which facilitates the process of communication and enables a set of agents to reach a consensus about various issues. This consensus might imply the emergence of effective social norms or trust allowing the establishment of common expectations as forms of social capital within a population of agents.

  2. A further set of experiments shows that the critical interval \(\Delta \theta \) again increases with the difference between consumers’ initial beliefs and does not vary with the direct influence exerted by one consumer on the other (as claimed in Proposition 5).

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Acknowledgments

This research has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: Aristeia, SocioMine.

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Authors and Affiliations

  1. Department of Management Science & Technology, Athens University of Economics & Business, Athens, Greece

    Christos Bilanakos, Dionisios N. Sotiropoulos, Ifigeneia Georgoula & George M. Giaglis

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  1. Christos Bilanakos
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  2. Dionisios N. Sotiropoulos
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  3. Ifigeneia Georgoula
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  4. George M. Giaglis
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Correspondence to Dionisios N. Sotiropoulos.

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Bilanakos, C., Sotiropoulos, D.N., Georgoula, I. et al. Optimal Influence Strategies in Social Networks. Comput Econ 49, 517–561 (2017). https://doi.org/10.1007/s10614-016-9568-1

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