This summer Sam will work as an intern at Firm A. At the end of the summer internship, Firm A will offer Sam a permanent position at the ?rm. If Sam rejects the offer, he can then go to the job market, where Firm B and Firm C can simultaneously make offers to Sam. So the game is as follows. First, Firm A offers a wage wS to Sam. Sam can either accept or reject the offer. If Sam accepts, the game is over. If Sam rejects, then Firm B and Firm C secretly and simultaneously offer wages wA and wT to Sam. Sam can then accept Firm B's offer, or accept Firm C's offer, or reject both offers.
Sam can generate a revenue of 100 for Firm A but only of 50 for Firm B or Firm C. Wages can be any number greater than or equal to zero. The payoff to a ?rm is the revenue generated by Sam minus his wage if Sam accepts its offer, and zero if Sam rejects. The payoff to Sam is the wage offered by the ?rm where he accepts the offer, if he accepts an offer, and zero if he rejects all offers.
Assume that if Sam is indifferent between accepting and rejecting an offer at a given decision node, then he accepts. Also, assume that if Sam is indifferent between accepting Firm B's offer and accepting Firm C's offer, then he accepts Firm B's offer with 0.5 probability and Firm C's offer with 0.5 probability. [Note: This assumption has no effects on the results.]
a) Suppose that Sam rejects Firm A's offer and goes to the job market, where Firm B and Firm C make offers simultaneously. What offers will Firm B and Firm C make?
b) Consider now the whole game. What is the credible Nash equilibrium? Describe the players' strategies. What is the outcome of the game? [Note: You may draw the game tree, but you are not required to.]
c) Now suppose that before Sam starts his summer internship, he can take a course on consulting at UNIVERSITY. There are two consulting courses: corporate Firm A and general consulting. If Sam takes the corporate Firm A course, he can generate an extra revenue of 50 if he works for Firm A. (That is, he can generate revenues of 150 for Firm A, and of 50 for Firm B or Firm C.) If Sam takes the general consulting course, he can generate an extra revenue of 25 for any of the consulting ?rms. (That is, he can generate revenues of 125 for Firm A, and of 75 for Firm B or Firm C.) The ?rms can observe what course Sam decides to take. Taking a consulting course costs 10 to Sam (regardless of which course he chooses). Find the credible Nash equilibrium. Will Sam take a consulting course? Which one?
d) Consider the same setting as in part c), but now suppose that after the summer internship, it is Sam who makes an offer to Firm A about his wage wS. Firm A can either accept or reject the offer. (Assume that if Firm A is indifferent between accepting and rejecting an offer, then it accepts.) If Firm A accepts, the game is over. If Firm A rejects, then Sam goes to the job market where, as above, Firm B and Firm C secretly and simultaneously offer wages wA and wT to Sam. Everything else is the same as above. Will your answer to part c) change? Explain.