QUESTION 2 [16 marks] The market for teapots is currently monopolized by M. Consider the following sequential-move game. A potential competitor, E, must decide whether to enter the market (In) or not (Out). Entry costs R425 in set-up costs. Then M must decide on a High price (R3.50) or a Low price (R3.00) - these are the only possible prices. Market demand is Qa = 2000 - 400P, and cost of production (for either firm) is fixed at R2 per unit. If there are two firms in the market, the price chosen by M will apply to both firms and the market demand will be split equally between the two firms. The game tree below shows the profits earned by both firms as payoffs: -0, 900 High M Out Low 0 800 E High 25, 450 Low. 25, 400 2.1 Write down the backwards induction solution strategies for this game. [21 2.2 Represent the above game in strategic form (a payoff table) and use best response analysis to find all pure strategy Nash equilibriums (NE). Also indicate which of the NEs are subgame perfect NEs (SPNEs). [6] 2.3 The game now changes: Before E's choice, M can now choose to Invest in a new machine, which costs R850, that will reduce M's cost of production from R2 per unit to R1 per unit (E's cost of production remains R2 per unit). Alternatively, M can choose Not Invest and the unchanged original game will then be played. Provide an extensive-form representation (game tree) of the new game. Solve it using backwards induction and write down the solution strategies. [Hint: the new game has eight distinct outcomes.] [7] 2.4 Would M have chosen to invest if there were no threat of entry into its market? Briefly motivate. [1]