Evolution of conditional cooperation under multilevel selection

We study the emergence of conditional cooperation in the presence of both intra-group and inter-group selection. Individuals play public goods games within their groups using conditional strategies, which are represented as piecewise linear response functions. Accordingly, groups engage in conflicts with a certain probability. In contrast to previous studies, we consider continuous contribution levels and a rich set of conditional strategies, allowing for a wide range of possible interactions between strategies. We find that the existence of conditional strategies enables the stabilization of cooperation even under strong intra-group selection. The strategy that eventually dominates in the population has two key properties: (i) It is unexploitable with strong intra-group selection; (ii) It can achieve full contribution to outperform other strategies in the inter-group selection. The success of this strategy is robust to initial conditions as well as changes to important parameters. We also investigate the influence of different factors on cooperation levels, including group conflicts, group size, and migration rate. Their effect on cooperation can be attributed to and explained by their influence on the relative strength of intra-group and inter-group selection.