Stability and interaction in flatline games

Starting from a given one-shot game played by a finite population of agents living in flatline, a circular or constrained grid structured by the classical definitions of neighborhood, we define transformation rules for cellular automata, which are determined by the best-reply behavior in standard two-person symmetric matrix games. A meaningful concept of solution for the underlying population games will necessarily include robustness against any possible unilateral deviation undertaken by a single player. By excluding the invisible hand of mutation we obtain a purely deterministic population model. The resulting process of cellular transformation is then analyzed for chicken and stag-hunt type cellular games and finally compared with the outcomes of more prominent evolutionary models. Special emphasis is given to an exhaustive combinatorial description of the different basins of attraction corresponding to stable stationary states.