I have some issues with this problem in Game theory. I have attached a photo below 

9. It is common knowledge that player S's used car is Good with probability 1/2; otherwise, it is Bad. Of course, S knows whether her car is Good or Bad. A Good car would be worth $10,000 to her but a. Bad car only $6,000. S can keep her car or offer to sell it to B, who does not know whether the car is Good or Bad. Used cars sell for $12,000, and before offering to sell the car to B, 5 would have to Spend $1,000 to have it certied. A Good car would be worth $16,000 to B, but a Bad car would be worth only $9,000. This situation is modelled by the extensive game 09. Note that S and B are assumed risk-neutral, and all amounts are in $ thousands. Let 9 represent B's revised probability that the car is Good given that it is offered for sale (Le. that B's information set is reached). Dene mg,- to be the probability that 8 offers to sell the car given that it is Good, and dene 3:3 similarly. Let y be the probability that B decides to buy the car, given that it is offered for sale. Suppose that (530,173; y,q) is a Perfect Bayesian Equilibrium (PBE) of 09. (a) Using conditional probabilities as apprOpIiate, nd a condition relating 9', $3, and $3. (b) Calculate B's expected utility, given that B's information set is reached, as a function of y and g. (c) Show that S's expected utility if the car is Good equals Eusllc = 10 - rec.- + 2193;. Find S's expected utility if the car is Bad. ((1) Using (a) and appropriate derivatives of the expected utilities in (b) and (c), nd a PBE in which, whether her car is Good or Bad, S always o'ers to sell it to B. The Game G, [9. 0] Don't Offer (I *xo) [1], 4] [11, -3] Don't Buy (1 - y) Don't Offer (1 ' x3) [6, 0] [5, 0]