Before revision:  We model the different steady states, that are obtained in numerical simulations from the various update strategies, as different response strategy equilibria. These are then mapped to a generalized Ising model , describing the correlations between the players ' outcomes in a way that is agnostic to the existence of a link, but that coincides with the correlation device if there is one.
After revision:  We model the different steady states, that are obtained in numerical simulations of repeated games on networks until convergence is reached. As a result, correlations between the choices of the players emerge. Our approach is to study these correlations with a generalized Ising model , describing the correlations between the players ' outcomes in a way that is agnostic to the existence of a link, but that coincides with the correlation device if there is one.