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Theoretical and computational characterizations of interaction mechanisms on Facebook dynamics using a common knowledge model

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Abstract

Web-based interactions enable agents to coordinate and generate collective action. Coordination can facilitate the spread of contagion to large groups within networked populations. In game theoretic contexts, coordination requires that agents share common knowledge about each other. Common knowledge emerges within a group when each member knows the states and the thresholds (preferences) of the other members, and critically, each member knows that everyone else has this information. Hence, these models of common knowledge and coordination on communication networks are fundamentally different from influence-based unilateral contagion models, such as those devised by Granovetter and Centola. Moreover, these models utilize different mechanisms for driving contagion. We evaluate three mechanisms of a common knowledge model that can represent web-based communication among groups of people on Facebook, using nine social (media) networks. We provide theoretical results indicating the intractability in identifying all node-maximal bicliques in a network, which is the characterizing network structure that produces common knowledge. Bicliques are required for model execution. We also show that one of the mechanisms (named PD2) dominates another mechanism (named ND2). Using simulations, we compute the spread of contagion on these networks in the Facebook model and demonstrate that different mechanisms can produce widely varying behaviors in terms of the extent of the spread and the speed of contagion transmission. We also quantify, through the fraction of nodes acquiring contagion, differences in the effects of the ND2 and PD2 mechanisms, which depend on network structure and other simulation inputs.

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Notes

  1. A biclique contains two disjoint sets of nodes, where each node in one set has an edge to every node in the other set, while there are no edges between nodes in the same set. Examples include a cycle with 4 nodes (where each of the two disjoint sets has two nodes) and a star graph of size n where the center node (hub) is in one set, and the remaining \(n-1\) nodes (spokes) are in the other set.

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Acknowledgements

We thank the reviewer for providing helpful comments. This work is partially supported by University of Virginia Strategic Investment Fund award number SIF160, by NSF Grants CMMI-1916670 (CRISP 2.0), ACI-1443054 (DIBBS), IIS-1633028 (BIG DATA), CMMI-1745207 (EAGER), OAC-1916805 (CINES), CCF-1918656 (Expeditions), and IIS-1908530, and by the Air Force Office of Scientific Research under award number FA9550-17-1-0378. Any opinions, finding, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force.

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Authors and Affiliations

  1. Biocomplexity Institute and Initiative, University of Virginia, Charlottesville, VA, USA

    Chris J. Kuhlman, Gizem Korkmaz & S. S. Ravi

  2. Department of Decision Sciences, Bocconi University, Milan, Italy

    Fernando Vega-Redondo

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  1. Chris J. Kuhlman
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  2. Gizem Korkmaz
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  3. S. S. Ravi
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  4. Fernando Vega-Redondo
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Correspondence to Chris J. Kuhlman.

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Kuhlman, C.J., Korkmaz, G., Ravi, S.S. et al. Theoretical and computational characterizations of interaction mechanisms on Facebook dynamics using a common knowledge model. Soc. Netw. Anal. Min. 11, 116 (2021). https://doi.org/10.1007/s13278-021-00791-7

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