Social Network reciprocity as a social phase transition

We focus attention here on the "lattice reciprocity" mechanisms that enhance evolutionary survival of the cooperative phenotype in the Prisoner's Dilemma game when the population of Darwinian replicators interact through a fixed network of social contacts. Exact results on a "Dipole model" are presented, along with a mean-field analysis as well as results from extensive numerical Monte Carlo simulations. The theoretical framework used is that of standard Statistical Mechanics of macroscopic systems, but with no energy considerations. We illustrate the power of this perspective on social modelling, by consistently interpreting the onset of lattice reciprocity as a thermodynamical phase transition that, moreover, cannot be captured by a purely mean-field approach.

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