Payoff

 Bob is considering buying Ann’s car, which is equally likely to be in good condition, or with a hidden defect.  While Ann knows the car’s condition, Bob doesn’t, and cannot figure it out before actually buying it (as issues will become apparent to him only after a few months of driving).  Bob wants to make a take-it-or-leave-it offer to Ann.  He values the used car at$12,000 if it is in good condition, and at$8,000 if it has a defect.  He knows that Ann’s value for the car is$11,000 if it is in good condition, and$6,000 if it has a defect. Assuming that Bob maximizes his expected payoff and knows that Ann maximizes her own payoff, what will be his take-it-or-leave-it offer for her car?  Explain.