Though I haven't studied it using simulation runs, I did look briefly at some theoretical analysis from scaled up simulation runs with FEARLUS using innovation and imitation. For those who don't know FEARLUS, a more abstract equivalent model (for these purposes) would be described thus: Imagine a grid (or more generally, a network) of agents each choosing one of a finite number of options each time step. Each option has a return that changes over time, and agents have a satisficing choice algorithm: they will not change option unless the return from their last choice was below a threshold. (It should be assumed that each option has a change function ensuring its return is below the threshold of all agents at some point in time.) If they do decide to change, then they use a heuristic strategy to choose among the options. Innovative agents choose among the full set of options, whilst imitative agents choose only among the set of options last used by their immediate neighbours in the network. For the purposes of the following, it doesn't really matter how they do it.
When doing these studies in FEARLUS, we tended to use relatively small grids. In a simulation using purely imitative agents, eventually the agents would all use the same option. (I imagine it is possible to prove this using Markov Chains.) Once that happens the simulation is locked-in to that option as no (imitative) agent can choose an option not appearing in the network. However, depending on the rate of change of return from the options, I speculated that for a large enough network, it would be possible that no option would ever disappear from use. In particular, for an infinite network, assuming random initialisation, any arbitrarily-sized cluster of agents all using the same option is possible--a 'local lock-in', meaning that for any finite number of time steps, all options would persist. Thus, for a given number of time steps, it should be possible to specify a size of network at which the probability of an option disappearing is arbitrarily small.
In general I suspect that it should be possible to show that larger networks are more 'resilient' through maintaining a finite set of options among purely imitative agents for a longer period of time. (This would depend on network topology however--I suspect that there will be a relationship between the length of the shortest path and the resilience.) Regrettably I never got the time to study this to the point of preparing a publication...
I think this relates back to the work Laszlo was talking about earlier.
Gary
Gary Polhill
Research Scientist
The Macaulay Institute
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