I now realise you might be asking "how does this demonstrate hyperbolic, as opposed to exponential, discounting", which might be a valid point, but hyperbolic discounting does lead to discounting the future too heavily, so the player's choices do sort of make sense.

That is what I was wondering. Actually, exponential discounting values the (sufficiently distant) future less than hyperbolic discounting. Whether this is too heavy depends on the your parameter (unless you think that any discounting is bad).