Why is the halving a step function?

Why not let it be a smooth exponential decay?

Is there some game theory behind the choice of a four year cycle?

Has this topic been explored in the literature?

This question just struck me, reading that article about the GS banker's theory that Satoshi is the US and UK governments, he mentioned he believed the four year cycle lent evidence to the theory. I've never really questioned it, outside of being an arbitrary choice, why should it be a four-year step function rather than just a smooth decay? Both are equally predicable, which I think is the goal. What is gained by the unevenness?

Ooooh here's a wicked theory: it results in a predictable pattern that can be traded.