Collective phenomena in spatially extended evolutionary games.

A class of spatially extended evolutionary games with simple local rules is introduced. The emergent properties are studied through two complementary approaches. One is based on a heuristic local analysis, the other on exact global techniques. The local analysis provides criteria to group the games into classes with distinct behavior. The results facilitate numerical simulations and reveal that even simple games allow for complex spatio-temporal phenomena. The global analysis demonstrates that certain games perform an uphill march in a fitness landscape determined by the payoff parameters and the topology of the underlying lattice structure. For generic game parameters, the landscape is rugged owing to competing interactions and generates dynamical phenomena well known from frustrated systems: trapping in local maxima for noiseless dynamics and very long relaxation times for stochastic dynamics. Although the model is a mere caricature of evolutionary processes, some of its emergent properties are reminiscent of those observed in nature. It is argued that similar dynamical phenomena will be present in more elaborate approaches.