Time Average Replicator and Best-Reply Dynamics

where K is the set of pure strategies, ∆ = ∆(K) is the set of mixed strategies (the simplex on K), e is the k unit vector in ∆, xt ∈ ∆ is the composition of the population at time t with x k t denoting the frequency of strategy k. It was introduced by Taylor and Jonker [25] as the basic selection dynamics for the evolutionary games of Maynard Smith [20], see Hofbauer and Sigmund [16] for a summary. The interpretation is that in an infinite population of replicating players, the per capita growth rate of the frequencies of pure strategies is linearly related to their payoffs.