Generous Banker

You are at the bank and it is your lucky day. The banker is going pick random positive integer and you are too. You are both allowed to determine the probability distribution on the positive integers that you select from. If you and the banker select the same value, say $n$, you receive $n^2$ dollars. Otherwise, you receive nothing. Neither party knows the distribution the other selected. Assuming optimal strategy from both parties, what is your expected payout from this game? The answer will be in the form $\dfrac{a}{\pi^b}$ for integers $a$ and $b$. Find $ab$.