Consider a seller of a used car and a potential buyer of that car. Suppose that quality of the car, 6, is a uniform draw from [0, 1]. This quality is known to the seller, but not to the buyer. Suppose that the buyer can make an offer 32 6 [0,1] to the seller, and the seller can then decide whether to accept or reject the buyer's offer. This sounds like a dynamic game, but we can think of it as simultaneous move if we think of the seller as announcing the set of all prices she will accept and all those she will reject.) Payoffs are as follows: a _ p if o'er accepted, 3 6 ifoer rejected ' and 'J u _ a, + ()9 p if offer accepted, 5 _ 0 if o'er rejected Assume that a E [0, 1), that b 6 (0,2) , and that a + b > 1. These assumptions imply that for all 6, it is more eicient for the buyer to own the car. Show the following result: Proposition 1. The unique BNE is for the buyer to offer p = 531; and the seller to accept if and only if P 2 6