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1. Theoretical and Computational Characterizations of Interaction Mechanisms on Facebook Dynamics Using a Common Knowledge Model

   Kuhlman, Chris J; Korkmaz, Gizem; Ravi, S.S.; Vega-Redondo, Fernando (January 2021, Social network analysis and mining)

   null (Ed.)

   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, dierences in the effects of the ND2 and PD2 mechanisms, which depend on network structure and other simulation inputs. 

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2. Interaction Mechanisms on Facebook Dynamics Using a Common Knowledge Model

   https://doi.org/10.1007/978-3-030-65347-7_33  

   Kuhlman, C.J.; Korkmaz, G.; Ravi, S.S.; Vega-Redondo, F. (December 2020, Complex Networks & Their Applications)

   null (Ed.)

   Web-based interactions allow agents to coordinate and to take actions (change state) jointly, i.e., to participate in collective action such as a protest, facilitating 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 types (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. Common knowledge arises in many settings in practice, yet there are few operational models that can be used to compute contagion dynamics. Moreover, these models utilize different mechanisms for driving contagion. We evaluate the three mechanisms of a common knowledge model that can represent web-based communication among groups of people on Facebook. We evaluate these mechanisms on five social (media) networks with wide-ranging properties. We demonstrate that different mechanisms can produce widely varying behaviors in terms of the extent of contagion spreading and the speed of contagion transmission. 

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3. Effect of Interaction Mechanisms on Facebook Dynamics Using a Common Knowledge Model

   Kuhlman, Chris J; Korkmaz, Gizem; Ravi, S S; Vega-Redondo, Fernando. (January 2020, International Conference on Complex Networks and their Applications (Complex Networks))

   null (Ed.)

   Web-based interactions allow agents to coordinate and to take actions (change state) jointly, i.e., to participate in collective ac- tion such as a protest, facilitating 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 types (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. Common knowledge arises in many settings in practice, yet there are few operational models that can be used to compute contagion dynamics. Moreover, these models utilize different mechanisms for driving contagion. We evaluate the three mechanisms of a common knowledge model that can represent web-based communication among groups of people on Facebook. We evaluate these mechanisms on ve social (media) networks with wide-ranging properties.We demonstrate that dierent mechanisms can produce widely varying behaviors in terms of the extent of contagion spreading and the speed of contagion transmission. 

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4. Learning Common Knowledge Networks Via Exponential Random Graph Models

   Liu, Xueying; Hu, Zhihao; Deng, Xinwei; Kuhlman, Chris J. (January 2024, Proceedings of the International Conference on Advances in Social Network Analysis and Mining)

   Common knowledge (CK) is a phenomenon where each individual within a group knows the same information and everyone knows that everyone knows the information, infinitely recursively. CK spreads information as a contagion through social networks in ways different from other models like susceptible-infectious-recovered (SIR) model. In a model of CK on Facebook, the biclique serves as the characterizing graph substructure for generating CK, as all nodes within a biclique share CK through their walls. To understand the effects of network structure on CK-based contagion, it is necessary to control the numbers and sizes of bicliques in networks. Thus, learning how to generate these CK networks (CKNs) is important. Consequently, we develop an exponential random graph model (ERGM) that constructs networks while controlling for bicliques. Our method offers powerful prediction and inference, reduces computational costs significantly, and has proven its merit in contagion dynamics through numerical experiments. 

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5. A Successive Analysis of Online Networked Common Knowledge Experiments

   He, Hao; Liu, Xueying; Kattampallil, Neil; Lancaster, Vicki; Korkmaz, Gizem; Kuhlman, Chris J; Deng, Xinwei (September 2024, IEEE)

   Common knowledge (CK) is a phenomenon where a group of individuals each knows some collection of information, and, in essence, everyone knows that everyone knows the information. There are many applications involving CK, including business decision making, protests and rebellions, and online advertising. CK can lead to contagion and collective action but in ways that are fundamentally different from classic (e.g., Granovetter) threshold models used in the social sciences. Researchers developed CK models to enable the computation of contagion in networked populations. But these models have largely not been investigated using experiments with human subjects. In this work, we conduct a successive analysis of online CK experiments. We devise a flexible and interpretable statistical method to investigate the effects of significant factors, such as network structure and communication type. Among our findings, we demonstrate a phase change in group payout in the games that is caused by prohibiting player communication. 

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