5. Two risk neutral bidders, bidder A and bidder Z, participate in an auction for a single object. The private value of the object for each bidder is independently and uniformly distributed over the interval [0,1]. The auction proceeds as follows: The bidders submit their bids simultaneously; the highest bidder wins (if they tie, then the winning bidder is chosen randomly); if the bidder A wins, then he pays his bid; if the bidder Z wins, then she pays the bidder A's bid. (In this sense, the auction is biased in favor of the bidder Z.) Find an equilibrium of this auction with linear bidding strategies