A Simple Model of Global Cascades on Random Networks

There is no direct link to the paper I referenced.  It can be easily accessed here:  http://research.yahoo.com/node/2393 by clicking on the link under “download.”

A spark starts a forest fire.  A sick person infects a whole community.  Molly Ringwald’s tube socks become a generation’s tube socks.  Markets teeter on the edge and then tumble with a slight push. 

The concept of something “catching on” in a manner that becomes all encompassing is something of which we are all viscerally aware.  One would think that as the complexity and connectedness of everything around us increases that it would be critical to understand these cascading events.  Yet the academics and policymakers that control the economic levers of our country don’t even believe such events can occur.  Instead their models rely on rationality, normal distributions, and if all else fails what economists lovingly call a “fudge factor.”

There are many different terms across the fields of knowledge describing these events.  They are called quantum levels, phase changes, and tipping points.  The common thread through these concepts is they break free of the static nature of equilibrium into a world of dynamic systems.

Columbia University professor Duncan Watts’s works introduced me to the concept of the networked model.  I present his 2002 work “A Simple Model of Global Cascades on Random Networks.”  As the title suggests it is an extremely stripped down networked model where each node is a binary 1 or 0.  Each node is assigned a threshold where if % of their neighbors change then they themselves change (to either 0 or 1).  Then as Watts describes, “we construct a network of nodes, in which each node is connected to X # of neighbors with Y probability and the average number of neighbors is Z.”  Wikipedia will help fill in the Y and Z:

In the study of graphs and networks, the degree of a node in a network (Z in above) is the number of connections it has to other nodes and the degree distribution (Y in above) is the probability distribution of these degrees over the whole network. http://en.wikipedia.org/wiki/Degree_distribution

Fantastic experiments are now possible where one can manipulate the number of connections between agents, the interconnectedness of the system, and the source of the change.  But the real power of this model is that it is a world we recognize.  Sometimes a very well connected node can almost single handedly spread a cascade event.  Other times the more individual nodes have in common with each other the more frequent cascades despite the limited connectivity of any individual node. 

Now ask yourself, how many economic models of the types taught today could even begin to explain those occurrences?  How many different equilibrium models with how many different fudge factors would one have to construct to capture all the possible outcomes?

No model is perfect, but some are useful.

The spirit animal for this forum topic is the Antelope

The theme song for this forum topic is D4L – Scotty  http://www.youtube.com/watch?v=x1Ud-yEeSgc