Globogym has a monopoly over the market for personal training and faces a demand curve modelled as P = 400 – 0.2Q where P is the price of a training session and Q is the number of sessions provided. Their total cost function is given by TC = 1000 + 40Q. Let's assume that the Average Joe's gym enters the market as a competitor providing personal training sessions. In the first year of operations, Globogym and Average Joe's made their decisions about pricing simultaneously. Each firm chooses either pricing high or pricing low, and their interaction is represented in the game table below. The payoff to Globogym is represented in the table by tl, and the payoff to Neotel is represented by r). Average Joe's Price High Price Low Price High TI) = 160 I) = 300 TT = 240 T = 0 Globogym TI) = 0 TT) = 40 Price Low T = 300 T| = 160
3.1 Do either of the two telecommunications firms have a dominant strategy in this interaction?
If so, what are these dominant strategies?
3.2 What is the Nash Equilibrium of the game above? Clearly, show the logic you use to reach
your conclusion. What type of game is this?
3.3 Suppose the two firms could incentivize or punish each other, could the two firms find their
way to the socially optimum outcome? How would they do this?
After observing the strategic interaction between Globogym and Average Joe’s, the government
decides to pass a law that states that the two terms must pre-commit to the quantities of training
sessions they will supply to the American market.
Market
cost of production is constant at R40 per call. Let the number of sessions provided by Globogym be
represented by ?G and the quantity provided by Average Joe’s be represented by ?A.
3.4 Solve the firms’ reaction functions and graph them. How many sessions should Globogym
offer if Average Joe’s offers 100 sessions?
3.5 Since Globogym operated in the market before Average Joe’s, it is allowed to make the first
move. Calculate the number of telephone calls supplied by each firm, as well as the market
price and quantity of calls.
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