Boeing is planning a major new mid-range passenger plane, the Boeing 797, with many details under development, including the choice of maximum seating capacity. In the end, Boeing will choose either 200, 250 or 300 seats. This plane is expected to replace the iconic 737 as the highest-selling Boeing of all time, with over 5000 planes expected to be sold. Recaro is a major manufacturer of aircraft seats and is itself debating switching from making seat frames using aluminum to a titanium alloy, which would be 75% lighter.

Boeing's anticipated profits, if Recaro sticks with aluminum seats, would be $3b for the 200 seat design, $3.4b for the 250 seat option and $2.8b for the 300 seat plane. If Recaro doesn't invest in the new titanium technology, then Recaro's profits are $1m times the number of seats Boeing decides that the 797 should accommodate.

The new technology involves a new fixed R&D cost for Recaro but they can charge more per seat. With the 200 seat option, Recaro would only earn 50m from selling titanium seats, if Boeing chooses the 250 seat design Recaro makes $200m, while the 300 seat option would give Recaro profits of $400m. If Recaro does make the titanium seats available, the Boeing 797 will have better fuel efficiency and thus Boeing would make 3.2b from the 200 seat plane, 4b from the 250 seat option and 3.6b from the 300 seat design.

a. Construct a payoff table for the Boeing/Recaro 797 game. [Hint: Boeing has three strategies to consider based on seating capacity while Recaro has two based on their "metal choice."]

b. Does Recaro have a dominant strategy? Does Boeing have a dominant strategy? Explain.

c. What is the Nash equilibrium of this game?

d. Suppose Boeing acquires Recaro. Would the merged firm make the same choices that you predicted would occur in part c above? Explain.

e. [For this question ignore part d.] Suppose Boeing is able to commit to its choice FIRST and then Recaro makes its decision. Determine the Nash Equilibrium of this game.