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Direct reciprocity between individuals that use different strategy spaces

Fig 3

Evolutionary dynamics of memory spaces.

To explore the evolution of different memory capacities, we use replicator dynamics [50]. Members of a population can have one of three different memory spaces, memory-1 (), reactive (), or unconditional (). The fraction of population members with a given memory space changes in time, depending on whether players with this memory space obtain an expected payoff above average. a, When only two memory spaces compete, there are three possible dynamics: either one space is globally stable (dominance), each space is locally stable (bistability), or the two spaces form a stable mixture (coexistence). b, Here we illustrate our approach by considering an environment in which cooperation is comparably costly and where selection is relatively weak. c-e, We first analyze the replicator dynamics for each pair of memory spaces. We find that in a pairwise competition, dominates both and , whereas dominates . f, In a next step, we study the replicator dynamics among all three memory spaces. For the given parameter values, we find that is globally stable: independent of the initial composition of the population, all trajectories lead towards a monomorphic population of reactive players. Overall, we obtain a ‘memory dilemma’: the memory space that evolves is not the memory space that maximizes the population’s average payoff.

doi: https://doi.org/10.1371/journal.pcbi.1010149.g003