Journal on Policy and Complex Systems
b . If Agent X is a spreading type , the same process holds , except Agent X evaluates cells with respect to which has the lowest n .
4 . Once Agent X has chosen to move or stay , Agent X then considers it utility K X
. If K X
< θ then Agent X switches , that is , changes type with some probability r , where in a purely nonflexible case r = 0 .
5 . The current time step concludes .
At the conclusion of the time step , a new one begins with Agent X again considering all current relevant neighbors . If Agent X changed types in the previous time step , Agent X now plays this new time step as this new type . If we allow some probability q for environmental turbulence , v may take on a new value . Moreover , the neighbors may have changed locations and types — though only types affect utility calculations in given round .
One run of the model is 50 time steps . For nearly all runs in the analysis that follows , 50 was more than enough to reach convergence to a fixed ratio of types in each population as well as to establish a clear type winner ( the type with the highest group utility K U for that particular run ). For the few cases where even after 50 time steps there was not clear convergence , this lack of convergence was only with respect to group utility outcomes . That is , it was not necessarily clear by 50 time steps which type would emerge with the highest K G
. However , for all runs the long-run distribution of types converged within the first 10 – 20 time steps . This will be clear in the graphs discussed in the “ Results ” section .
The parameters of the model are summarized in Table 1 .
Table 1 . Parameters of the model
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