Game Theory Midterm Exam

Tonight I had a game theory midterm exam. Here are the first two questions (which were also the two easiest)...

1. "Competitive Bidding" Suppose two identical consulting firms (McKinsey & Boston Consulting Group) compete for the same client (Coca-Cola, Inc.) for which they propose to provide advisory services related to a possible merger. Each firm has an equal and constant marginal cost to provide the consulting services, c. Firms make competitive bids, simultaneously, to the client indicating the price at which they will provide the consulting work, b. The client will choose the lowest bid. If firms offer the same bid, assume they both expect to win the client with equal probability of 1/2 each. (a) Depict a strategic form game for this scenario. (b) Draw the best responses for both firms on one graph. (c) Identify all Nash equilibrium outcomes. (d) Now assume that firm one is more efficient than firm two so that if it wins the client, it will receive c1 < t="0,1,2,....">5, and
Q=q1+q2.
C1=1 and c2 = 3.

(a) Depict this industry in Extensive Form as a dynamic game. (b) Find a subgame perfect Nash equilibrium for this game. (c) In your equilibrium, which firm will exit the industry (produce no product) first? What is the logic behind this result?

Now suppose the firms face the same declining demand and have the same marginal cost c1 = c2 = 1, but each can only either produce a fixed quantity (firm 1's q=2, firm 2's q=1).

(d) Find a subgame perfect Nash equilibrium for this game. (e) In your equilibrium, which firm will exit the industry first? How does the result compare to that in (c) above?