The payoffs to each firm (in billions) are listed on the following diagram and an extensive form game between BP and Shell. BP has 20% of the U.S. gasoline market share and Shell has 16% market share. BP and Shell are attempting to determine whether to send geologists to explore Oil Track 50.
(a) What is the Nash equilibrium (or equilibria) in this game?
(b) Determine the Nash equilibrium that satisfies backward induction.
(c) You are called in to advise BP on whether they should pursue a merger with Shell in which case they could coordinate their actions. What is your advice to BP?