Complex Networks from Other Dynamic-Dependent Attachment Rules

In this chapter, we will continue exploring the issue of the entanglement between the growth of a complex structure and the dynamics that is taking place on top of it simultaneously, in such a way that the outcome of the game, meaning the benefits the nodes get out of the interaction, will affect the probability of the existing nodes to attract links from newcomers. So we will work with a model similar to the one introduced in Chap. 7, but with two important differences: on the one hand, the dependence of the probability of attachment will be exponential with the fitness of the nodes, instead of linear. On the other hand, we will also modify the imitation rule to a Fermi-like function, instead of using a Replicator-like probability, so irrational changes of strategy will be allowed now, meaning that a node can imitate a neighbor whose payoff is lower than its own.

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