We study the conditions in which the unbounded growth of complexity – measured in terms of expressed genome size – can be observed in coevolving populations of neural agents involved in different classes of interactions. To reproduce the results of prior work on the dynamics of open-ended evolution, we introduce a simple pursuit-evasion scenario that allows for the development of increasingly intricate strategies. It is shown that for some configurations of our game, fitness-proportionate selection leads to stagnation while more sophisticated coevolutionary methods produce apparently unbounded complexity growth. Analysis of behavioral patterns sheds some light on the evolutionary pressures introduced by the model. Our findings replicate many features of previously reported work; however, we observe particular dynamics that differ in important respects, challenging prior conclusions, creating new opportunities, and highlighting the need for further investigation of this domain.