Exercise 2bis - Contestable market result

Consider an industry where there is an incumbent firm, I, and another firm, E, which has never been active in the industry but is considering entering it. Both firms sell the same identical product and have the same costs: when they produce and sell, they incur a fixed cost f, and a marginal costs c. (Note that f does not change with the number of units, whereas c does.) Consumers are identical and their demand is Q=Q(p). If both firms were active and chose the same price, each firm would receive half demand. The game being played is as follows. At the first stage, firm I chooses its price pI. At the second stage, after having observed I's choice, firm E sets its price pE. Consumers observe both prices and decide from which company to buy; all transactions take place.

Q1) Find the sub-game perfect Nash equilibrium of the game.

Q2) Discuss the result obtained. In particular, comment on the role of the fixed cost f and on the timing of the price decisions.