Consider a second-price wallet auction. The auction is for a pot of money equal to the sum of the cash in each of the bidders' wallets. Each bidder can check how much money they have in their wallet but not in their rivals' wallets.

Let Xi denote how much cash bidder i has in his wallet. Suppose each Xi is independently and identically distributed uniformly on [0, 100]. Each bidder's value for the pot is given by Vi = Xj.

Suppose there are 2 bidders. Show that bidder 1 bidding 1(x1) = 10x1 and bidder 2 bidding 2(x2) = 10/9 x2 is a BNE.