How Trend Followers Affect Cascades on Random Networks

Summary

This paper extends a threshold model of collective behavior to include global nodes, or trend followers. In a standard local cascade, a node activates in response to its neighbors; in this extension, some nodes also respond to the overall fraction of activated nodes. The model examines how local influence and population-wide trends interact as behavior spreads through a network.

The analysis finds that global nodes can speed up a cascade after a trend has formed, while making it less likely for that trend to emerge in the first place. Their net effect can therefore be either to encourage or inhibit cascades, and the model suggests that an intermediate share of trend followers may maximize average cascade size. This is a theoretical network result about collective behavior, not evidence of a trading signal or a market strategy. The provided description does not specify empirical calibration or show that the result holds for real financial markets.

Key ideas

• The model adds nodes whose activation depends on the population-wide share of active nodes.
• Global trend following can accelerate a cascade once a trend has emerged.
• The presence of trend followers can also reduce the chance that a trend emerges.
• An intermediate proportion of trend followers may maximize average cascade size in the model.
• The description gives a theoretical result without evidence of direct trading performance.

Tags

# Trend-driven information cascades on random networks


# Trend-driven information cascades on random networks









Threshold models of global cascades have been extensively used to model real-world collective behavior, such as the contagious spread of fads and the adoption of new technologies. A common property of those cascade models is that a vanishingly small seed fraction can spread to a finite fraction of an infinitely large network through local infections. In social and economic networks, however, individuals' behavior is often influenced not only by what their direct neighbors are doing, but also by what the majority of people are doing as a trend. A trend affects individuals' behavior while individuals' behavior creates a trend. To analyze such a complex interplay between local- and global-scale phenomena, I generalize the standard threshold model by introducing a new type of node, called \textit{global nodes} (or \textit{trend followers}), whose activation probability depends on a global-scale trend; specifically the percentage of activated nodes in the population. The model shows that global nodes play a role as accelerating cascades once a trend emerges while reducing the probability of a trend emerging. Global nodes thus either facilitate or inhibit cascades, suggesting that a moderate share of trend followers may maximize the average size of cascades.

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