We study agent societies where self-interested agents interact repeatedly over extended time periods. In particular, we are interested in environments where agents can form mutually beneficial relationships by exchanging help but an agent would rather receive help than give it. Evolutionary tournaments with competing help-giving strategies can model scenarios where agents periodically adopt strategies that are outperforming others in the population. Such experiments, however, can be computationally costly and hence it is difficult to prescribe a rational strategy choice given environmental conditions like task mix, strategy distribution in the population, etc. A preferred approach, pursued in this paper, is to analytically capture the dynamics of the strategy mix in the population under an evolutionary tournament. Such an analytical model can be used to predict the evolutionarily dominant strategy, the rational strategy choice. Categories and Subject Descriptors I.2.11 [Artificial ...