Effects of sampling interaction partners and competitors in evolutionary games

Abstract

The sampling of interaction partners depends on often implicit modelling assumptions, yet has marked effects on the dynamics in evolutionary games. One particularly important aspect is whether or not competitors also interact. Population structures naturally affect sampling such that in a microscopic interpretation of the replicator dynamics in well-mixed populations competing individuals do not interact but do interact in structured populations. In social dilemmas interactions with competitors invariably inhibit cooperation while limited local interactions in structured populations support cooperation by reducing exploitation through cluster formation. These antagonistic effects of population structures on cooperation affect interpretations and the conclusions depend on the details of the comparison. For example, in the Snowdrift game, spatial structure may inhibit cooperation when compared to the replicator dynamics. However, modifying the replicator dynamics to include interactions between competitors lowers the equilibrium frequency of cooperators, which changes the conclusions and space is invariably beneficial, just as in the Prisoner's Dilemma. These conclusions are confirmed by comparisons with random matching models, which mimic population structures but randomly reshuffle individuals to inhibit spatial correlations. Finally, the differences in the dynamics with and without interactions among competing individuals underlies the differences between death-birth and birth-death updating in the spatial Moran process: death-birth supports cooperation because competitors tend not to interact whereas they tend to do for birth-death updating and hence cooperators provide direct support to competitors to their own detriment.