Derive the bidding strategies in BNEFind the resulting allocation scheme

Question 4 (Auction, 15%, 30min). Consider an auction that is just like the first-price sealed-bid auction, except that the item's price/payment is 2/3 of the highest bid instead of the highest bid; the item still goes to the highest bidder. Other rules remain the same. There are only two buyers, i = 1,2, each having a linear bidding strategy b; (0;) = a;0; and linear utility function u; (x;, 01) = 0ix; - ; where x; = 1 or 0, and c; is the payment, where a; > 0 is a constant. The buyers' private valuations 0, and 02 are drawn independently from the uni- form distribution on [0, 1]