How cooperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model to take into account the spatial dimension in evolutionary games is in terms of cellular automata with just a one-parameter payoff matrix. Here, the effects of spatial heterogeneities of the environment and/or asymmetries in the interactions among the individuals are analysed through different extensions of this model. Instead of using the same universal payoff matrix, bimatrix games in which each cell at site (i, j) has its own different ‘temptation to defect’ parameter T(i,j) are considered. First, the case in which these individual payoffs are constant in time is studied. Second, an evolving evolutionary spatial game such that T=T(i,j;t), i.e. besides depending on the position evolves (by natural selection), is used to explore the combination of spatial heterogeneity and natural selection of payoff matrices.
