The "Guess $\frac{2}{3}$ of the average" is a game where $k$ people choose a number between 0 and 100 inclusive, and the person with the closest answer to $\frac{2}{3}$ of the average wins. It is clear that there is a Nash equilibrium, in which everyone picks the number 0.
Here's the twist - the payoff that you get for winning is equivalent to the number you picked at the start, divided by how many people picked your number. So you would get 0 dollars. Obviously, you would want to maximise your payoff.
I'd assume that the Nash equilibrium is still 0 dollars. However a rational choice that would yield money is if everybody picked 100 dollars - and so everybody would get 1 dollar.
Is there a better strategy to this game?