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Continuous Cascading Process

In this blog, I focus on how an individual’s choices depend on what other people do—using probabilities to model individual’s preference, rather than giving a discrete label as in the traditional cascading model of our book.

In the traditional cascading model, one of the solution to make a complete cascade is to decrease the threshold for adopting new technique by increasing its payoff. In reality, there exists another scenario that makes the payoff of new techniques significantly larger than old ones, for example, the new version of Windows operating system and the old ones. The new operating system is generally more stable, secure and fancy than the old one, thus can easily propagate to every corner of the network. In this study, I focus this type of cascading, modeling the irresistible new technique which has significantly large payoff by slightly modify diffusion criteria, the probability of new technique strengthen itself in each time steps.

Model Definition (I edit part of content in word for sake of formulas)

 

Experiment Result

In this experiment, I construct a connected-graph with 2 local clusters, and the new technology emerging in the left corner of one cluster ( the black one), the payoffs for new technology and old technology are 2, 1 separately. I use greyscale to represent P_A, As it shows in above figure, black node (P_A=1) gradually penetrates to another densely-connected structure.

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