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I am studying network formation models and I have seen the separation of those models into two groups (wikipedia):

  • Agent-based models:

Aka game-theory based models. This distinction makes sense to me. But it mentions a "fixed number of players". Are there no game theoretic models with a dynamic number of players?

  • Dynamic models:

These seem to be the ones not involving game theory. But as the name suggests they are categorized by their dynamic number of nodes.


So where do game theoretic models with a dynamic number of nodes fit? Are they in both classes? Why is the Erdös-Rèny Model considered dynamic? Where does this categorization come from? Why not simply use game-theoretic and non-game-theoretic as a categorization as is implied in the wiki article?

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I think you're taking the list in Wikipedia too seriously. It's not a statement that "all possible methods fall into exactly one of these two categories". Rather, it's a rough categorization that might be helpful in rapidly getting a first overview of the field. Often a categorization exists because it is useful and does a reasonable job of capturing many of the methods in the literature. Categorizations don't have to cover the entire space of possible methods to be useful.

Of course one could have other categorizations, but they might lend less insight into the kinds of methods that are most typically used or studied.

Wikipedia even mentions the possibility of combining both methods in the very article you linked to: https://en.wikipedia.org/wiki/Network_formation#Growing_networks_in_agent-based_setting.

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