You could've made this a recursive loop, like unstoppable force vs immovable object. In that case the growth rate follows a sinusoidal trajectory like A + B(sin Cx) and this model predicts who is leading in any given scenario as the time complexity to get from one state of growth to another is O(sin x) this follows the expected sinusoidal behaviour of growth, with a bit of added noise to account for randomness. But this randomness always converges to zero which is pretty cool