Consider two firms, A and B, where A is a potential entrant and B is the incumbent

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Question:

Consider two firms, A and B, where A is a potential entrant and B is the incumbent in the industry.

They play the following sequential game: First A decides whether to enter (E) or to not enter (N), and then B decides whether to produce high (H) or low (L) output. The payoffs from the game are given in the game tree below:

E N

H L H L

-2,5 6,6 0,12 0,8

a. List all the available strategies for firm A and firm B.

b. What is (are) the pure strategy Nash equilibrium of this game?

Had firm B built a larger factory, it would have had higher fixed costs, but lower marginal costs. The payoffs would then have been as in the game tree below:

E N

H L H L

-2,4 6,3 0,11 0,5

c. What is the perfect Nash equilibrium of this game?

Now consider the following three stage game: First B decides whether to build a small or large factory, then A decides whether or not to enter and then B decides whether to produce high or low output.

d. Show the game tree for this three-stage game.

e. What is the subgame perfect Nash equilibrium (using backward induction) of this game? Explain.