A has an IID uniform distribution in [0,6] for item X. B has an IID uniform distribution in [2,4] for item X.
There is an auction X, highest bidder wins and pays what they bid. The player's payoff is their value minus their bid, v-b. If they don't have the highest bid, they don't win the auction and get payoff of 0. The distributions are common knowledge but the realization is unknown. (for example B knows that A has a value between 0 and 6 but does not know that it is a 4.)
What is the expected payoff of A and B when they play their optimal strategies?