Problem 5 (2 +2 + 5 + 3 = 12 marks) Your SuperBBA drink, which increases short-term brain activity, has been very profitable. However, Steve was able to reverse-engineer your recipe and is now selling the same drink under a different name, the PowerBBA drink. So you have to share the market with Steve. At 8am every day, you and Steve each announce your price (high or low) simultaneously and sell drinks at these prices all day. There is no brand loyalty among drink buyers. Your daily profits (in $) under each set of strategies are as follows: Steve N Low price 200, 200 1000, 0 High price 0, 1000 400, 400 a) Assume that you and Steve play the game only once (i.e. for one day). What is the equilibrium of the game? Are your and Steve's joint payoffs maximized? What kind of game is this? b) Assume that you and Steve will be selling drinks each day for the next 30 days. What will the resulting equilibrium pricing strategies for each day be? Explain briefly. c) Suppose that you and Steve compete for an indefinite number of days, and that neither of you knows how long your competition will last. You adopt a grim trigger strategy to encourage Steve to \"cooperate\". Steve is very impatient, with a daily discount rate r = 0.25. Would he cooperate? What is the highest level of impatience for Steve the highest discount rate r that he might have such that you could still elicit cooperation from Steve? d) Suppose that you and Steve play the game only once, but that you set and commit to your price first, and that Steve sets his price after having observed your price. Draw the game in extensive (1.e. game tree) form. What is the equilibrium of this game? Briefly explain. Do you have a first-mover advantage in this game? Why or why not