1. (Extensive Games with Perfect Information. ) The only two firms moving crude oil from an oil-producing region to a port in Atlantis are pipelines: Starline and Pipetran. The following table shows the annual profit (in millions of euros) that each firm would earn at different capacities. Starline's profit is the left number in each cell; Pipetran's profit is the right number. At the current capacities (with no expansion ) Starline is earning 40 million euros, and Pipetran is earning 18 million euros annually. Each company is considering an expansion of its capacity. Sine Pipetran is a fairly small company, it can consider only a small expansion to its capacity. Starline has the ability to consider both a small and a large expansion. Pipetran No Expansion Small No Expansion 10,18 28,22 Starline Small 48,14 32,16 Large 38,10 24,5 (a) If the two firms make their decisions about expansion simultaneously, is there a unique Nash equilibrium? If so, what is it? If not, why not? (b) Would Starline have a firs-mover advantage if capacities were chosen sequent tially? If so, draw the game tree and briefly explain how it might credibly implement this strategy. (c) Suppose you were hired to advise Pipetran about its choice of capacity. If Pipetran has the option of moving first, should it do so? Draw the game tree and explain. 2. (Mixed Strategies.) Dorothy and Henry are playing one-stage game shown in the table below. Dorothy has three possible choices (Left, Middle, and Right), as does Henry (Up, Middle, and Down)