Simple interactive model of contagion

  1. Click ► to update time step
  2. Drag the time step bar to go back in time
  3. q, the payoff parameter, can be changed for each update if desired
  4. Progressive update means nodes cannot switch to old behaviour
  5. Reset creates a new random graph with parameter n and p, see here
  6. Hover over or drag nodes

This is a quick interactive tool based off the simplest model of cascading behaviour in a network (or rather, an abstract model of any network that can be represented as a graph). In essence each node plays a two player game with each of it's neighbours to determine it's state in the next time step. See "Cascading behaviour in networks" by Jon Kleinberg, in "Algorithmic Game Theory" by Nisan et al for some discussion.

Even in this simplest of models, we have some interesting questions, for example, given an initial set S and a graph G, is it decidable that S eventually turns all nodes in G to a particular state? (i.e S is contagious) If it is, what's the theoretical minimum bound complexity of this algorithm? How about more generalised models? Potential applications? Can I use it to entertain my cat? (Probably)

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