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On “Influencers” and Their Impact on the Diffusion of Digital Platforms

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Highlights of Practical Applications of Agents, Multi-Agent Systems, and Complexity: The PAAMS Collection (PAAMS 2018)


We simulate the impact of influencers in the adoption of digital multi-sided platforms. We consider four metrics to identify influencers: degree, betweenness, closeness and page rank, and we test how they shape the adoption, prices, and profits of digital multi-sided platforms using an agent-based model. We simulate the market adoption with and without those influencers. We find that adoption is lower and grows slower without influencers. This result is also valid even when one side has influencers, but the other one has not. Depending on the network we assume, the role of influencers is different. In some cases, the launching fails, in others, it is slower only. We also find that prices are sensitive to influencers. However, the effect on prices depends on which centrality measure we consider. Companies use prices as a tool to counterbalance the influence of influencers in profits. Lastly, we show that profits are very sensitive to influencers, without them, profits are lower.

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  1. 1.

  2. 2.

    Influencers can be passive or active. Active ones are those who are targeted by companies to promote their products. Passive ones are those who are not directly targeted by companies. In this work, we focus in passive influencers.

  3. 3.

    See for a global perspective [8, Chap. 7]. But there are examples in epidemiology, [15], network robustness, [11] or diffusion of information, [12].

  4. 4.

    The developers’ utility function is symmetric. Despite this symmetry, users value the number of developers on the platform, and developers the number of users. The platform has to be able to fix prices that attract both groups at the same time.

  5. 5.

    The parameter \(\delta _{u}\) controls how users value the presence of an additional developer. For simplicity’s sake and without loss of generality, we assume that this value is constant and equal for all users and developers, \(\delta _{u}=\delta _{d}=\delta \).

  6. 6.

    We define a period as an iteration in the simulation model. We choose one hundred iterations arbitrarily. Other number of iterations can be considered as well.

  7. 7.

    Profitability is measured in terms of net profits. In this framework, it is the sum of the revenues on users’ and developers’ sides. Formally: \(n_d * p_{d,j} + n_u * p_{u,j}\).

  8. 8.

    We choose 5% of innovators because it is a common assumption throughout the diffusion of innovation literature.

  9. 9.

    The probability depends on the normalized degree of each node. The higher the degree, the higher the chance of being infected. We divided the degree of each user/developer by 4. In this way, the most connected node will only be infected in 1 out of 4 cases.

  10. 10.

    The page rank of a node is the proportion of time that an agent walking forever at random on the network would spend at one node. Nodes that are connected to a lot of other nodes that are themselves well-connected get a higher page rank.

  11. 11.

    The experiment has been carried out by removing the 5% and 15% also. The conclusions are the same.

  12. 12.

    The number of users and developers is arbitrarily selected. We can consider other numbers, and conclusions will not change.

  13. 13.

    These networks are generated following the G(n, p) variant of the ErdõsRènyi model, the BarabàsiAlbert algorithm for preferential attachment networks, and the Watts-Strogatz small-world network. For each network topology, we simulate 150 runs.

  14. 14.

    We only consider the adoption, not the profitability. We will analyze it later.

  15. 15.

    Networks are critically damaged when we remove the influencers in the random and preferential attachment networks.

  16. 16.

    In the same simulations but without platforms fixing prices, the speed of infection is around 3–4% per iteration.


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Sanchez-Cartas, J.M., Leon, G. (2018). On “Influencers” and Their Impact on the Diffusion of Digital Platforms. In: Bajo, J., et al. Highlights of Practical Applications of Agents, Multi-Agent Systems, and Complexity: The PAAMS Collection. PAAMS 2018. Communications in Computer and Information Science, vol 887. Springer, Cham.

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