Question 1 [6 marks] Hayley wants to buy a car. The used-car salesman can sell her a good car I{for which he earns a small prot] or a lemon {for which he earns a large prot]. The payoffs {9c y] for each decision are indicated in the game tree below, with x being the Hayley's satisfaction and 1/ being the salesman's prot. Hayley No purchase Purchase Salesman (0,0) Lemon [5:5] (1l'8) a} Assume the salesman only cares about his prot. What would the salesman do if Hayley chooses to purchase? Why? [1 mark] bl Given the anticipated choice of the salesman, would Hayley purchase the car? Why? [1 mark] cl Suppose Hayley can take legal action if she is sold a lemon. If Hayley is successful in court, she will be refunded the purchase price but would suffer a cost of -5 due to the effort involved. Would this change the outcome? Why? [2 marks] d] Suppose Hayley has a reputation of being quick to anger and always carrying out her threats. Suppose Hayley would experience satisfaction of +6 from taking legal action (in addition to the effort cost of -5l. The salesman knows this and believes it to be a credible commitment. Would this change the outcome? Why? [2 marks]