If happiness is, e.g., log(money), then you can just adjust the game to have the payout be $2^2^n after the nth step. This cancels out the logarithm and recovers the paradox. The only way to get out of it with diminishing returns is to have happiness reach a finite asymptote.

When there is a decent probability that you may crash the financial system I'm nor even sure if a strictly monotonically increasing function is appropriate.