Replicator population dynamics of group ($n$-agent) interactions. Broken symmetry, thresholds for metastability and macroscopic behavior
We analyze from basic physical considerations the Darwinian competition for reproduction (evolutionary dynamics) of strategists in a Public Goods Game, the archetype for $n$-agent (group) economical and biological interactions. In the proposed setup, the population is organized into groups, being the individual fitness linked to the group performance, while the evolutionary dynamics takes place globally. Taking advantage of (groups) permutation symmetry, the nonlinear analysis of the "mesoscale" Markov phase space for many competing groups is feasible to a large extent, regarding the expected typicality of evolutionary histories. These predictions are the basis for a sensible understanding of the numerical simulation results of the agent (microscopic) dynamics. Potential implications of these results on model-related issues as, e.g. group selection, the role of "social norms", or sustainability of common goods, are highlighted in concise terms, before the conclusion.