Imagine a market setting with three firms. Firms 2 and 3 are already operating as monopolists in two different industries (they are not competitors).
Firm 1 must decide whether to enter firm 2's industry and thus compete with firm 2 or enter firm 3's industry and thus compete with firm 3. Production in firm 2's industry occurs at zero cost, whereas the cost of production in firm 3's industry is 2 per unit.
Demand in firm 2's industry is given by p = 9 - Q, whereas demand in firm 3's industry is given by p' = 14 - Q', where p and Q denote the price and total quantity in firm 2's industry and p and Q denote the price and total quantity in firm 3's industry. The game runs as follows: First, firm 1 chooses between E2 and E3 . (E2 means "enter firm 2's industry" and E3 means "enter firm 3's industry.") This choice is observed by firms 2 and 3.
Then, if firm 1 chooses E2 , firms 1 and 2 compete as Cournot duopolists, where they select quantities q1 and q2 simultaneously. In this case, firm 3 automatically gets the monopoly profit of 36 in its own industry. In contrast, if firm 1 chooses E3 , then firms 1 and 3 compete as Cournot duopolists, where they select quantities q= 1 and q= 3 simultaneously; and in this case, firm 2 automatically gets its monopoly profit of 81>4.
(a) Calculate and report the subgame perfect Nash equilibrium of this game. In the equilibrium, does firm 1 enter firm 2's industry or firm 3's industry?
(b) Is there a Nash equilibrium (not necessarily subgame perfect) in which firm 1 selects E2 ? If so, describe it. If not, briefly explain why.