There are three consulting firms hiring this year: Nous Group, BCG, and McKinsey. John will graduate from the MBA program at UoL and would like to find a job in consulting. John currently works as an intern at Nous. At the end of the internship, Nous will offer John a permanent position at the firm. If Chlo rejects the offer, she can then go to the job market, where BCG and McKinsey can simultaneously make offers to John. The game is as follows.First, Nous offers a wagewnto John.John can either accept or reject the offer. If John accepts Nous's offer, the game is over. If she rejects it, then BCG and McKinseysecretly and simultaneouslyoffer wageswbandwm. John can then accept BCG's offer (wb), or accept McKinsey's offer (wm), or reject both offers. John can generate a revenue of 100 for Nous but only of 50 for BCG or McKinsey. The payoff to a firm is the revenue generated by John, minus her wage if John accepts its offer, and zero if John rejects it. The payoff to John is the wage offered by the firm whose offer she accepts, and zero if she rejects all offers. As a tie-breaking rule assume that if John is indifferent between accepting and rejecting an offer at a given decision node, then sheacceptsit. Also, assume that if John is indifferent between accepting BCG's offer and McKinsey's offer, then she flips a coin to decide.

Q1.Suppose that John rejects Nous's offer and goes to the job market, where BCG and McKinsey make offers simultaneously. What offers will BCG and McKinsey make?

Q2. Consider now the whole game. What is the credible Nash equilibrium? Describe the players' strategies. What is the outcome of the game?

Q3. Now suppose that before John starts his summer internship, he can take a course on consulting at UoL. There are two consulting courses: corporate strategy and general consulting. If John takes the corporate strategy course, he can generate an extra revenue of 50 if he works for Nous. (That is, he can generate revenues of 150 for Nous, and of 50 for BCG or McKinsey.) If John takes the general consulting course, he can generate an extra revenue of 25 for BCG and McKinsey. (That is, he can generate revenues of 100 for Nous, and of 75 for BCG or McKinsey.) The firms can observe what course John decides to take. Taking a consulting course costs 10 to John (regardless of which course he chooses). Find the credible Nash equilibrium. Will John take a consulting course? Which one?

Q4. Consider the same setting as in part Q3, but now suppose that after the summer internship, it is John who makes an offer to Nous about his wage wn. Nous can either accept or reject the offer. (Assume that if Nous is indifferent between accepting and rejecting an offer, then it accepts.) If Nous accepts, the game is over. If Nous rejects, then John goes to the job market where, as above, BCG and McKinsey secretly and simultaneously offer wages wb and wm to John. Everything else is the same as above. Will your answer to part Q3 change? Explain.