Symmetry and collective fluctuations in evolutionary games

We review stochastic evolutionary game theory from a perspective that starts in the very general regression methods of population genetics, and introduces games as a powerful yet flexible framework to unpack the “black box” of development, which generates frequency-dependent fitness maps and which may also structure the transmission process. This approach to evolutionary game theory retains the robustness of regression methods while attempting to progressively refine mechanistic explanations. The tautological nature of normal-form games, and their refinement with the extensive form, are compared as characterizations of mechanism. We develop symmetry as the core concept to classify evolutionary game models, and symmetry breaking as the source of robust multiscale dynamics. Stochastic population processes generally produce regression models that depend on scale, and the change of parameters at different scales, as well as the emergence of hierarchical units of selection, is due to collective fluctuations. The current paper surveys aspects of symmetry in games, emphasizing qualitative features. A companion paper develops large-deviation methods for multiscale dynamics in evolutionary game theory, and presents quantitative solutions for some of the scale-dependent models in this paper.