am i correct in thinking that convertible notes can be thought of as a way of changing the equilibrium of prisoner's dilemma? i.e., by introducing a temporal element and rewarding early investors you avoid the equilibrium where everyone is waiting for everyone else (akin to the Nash equilibrium of prisoner's dilemma where both prisoners stay silent, instead you want both prisoner's to confess).
There's more to the game theory aspect, actually.
Since note holders get a better share with a lower valuation, it could cause collusion with the VCs...
I'd say that has nothing to do with convertible notes in particular. There are many ways/dynamics to employ to move things along a bit quicker. Convertible notes with different prices could be one, i.e. drop the first price lower. For equity rounds, you just give the first guy extra advisor shares, which does the same thing.