Consider a two period game where an incumbent monopolist in an industry fears entry in the second period. The demand for the product is given by P = 100- Q, where Q is the total quantity produced in the market. Suppose the incumbent has a marginal cost of $24, while the entrant has a marginal cost of $38. In addition, each firm incurs a fixed cost of $200 in each period that it is in business. The incumbent monopolist can either charge a monopoly price in period 1 or a limit price. In period 2 the incumbent monopolist can again charge either a limit price or an accommodating price. The potential entrant firm has two strategies: either to enter or stay out at the beginning of period 2 after observing the price charged by the incumbent in period 1.
a) Construct the extensive form of the game described above.
b) Compute the payoffs at each terminal node making the same assumption about the limit price as was made in class. The first number at each terminal node should be the total profit of the incumbent computed over the two periods. The second number should be the profit of the entrant.
c) Find out the subgame perfect Nash equilibrium of this game. Write down the strategy of each player carefully that gives rise to the SPNE keeping in mind that a strategy must specify an action at each node that a player may be called upon to play. Why doesn't an incumbent want to charge a limit price in this game?
d) In reality we do see firms charging a limit price or a predatory price. What can account for this behavior despite the opposite prediction of the above model?