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We extend our exploration of the dynamics of spatial evolutionary games [Nowak & May 1992, 1993] in three distinct but related ways. We analyse, first, deterministic versus stochastic rules; second, discrete versus continuous time (see Hubermann & Glance [1993]); and, third, different geometries of interaction in regular and random spatial arrays. We show that spatial effects can change some of the intuitive concepts in evolutionary game theory: (i) equilibria among strategies are no longer necessarily characterised by equal average payoffs; (ii) the strategy with the higher average payoff can steadily converge towards extinction; (iii) strategies can become extinct even though their basic reproductive rate (at very low frequencies) is larger than one. The equilibrium properties of spatial games are instead determined by “local relative payoffs.”

We characterise the conditions for coexistence between cooperators …