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 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, while 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, while demand in Firm 3's industry is given by p' = 14 - Q', where p and Q denote price and total quantity in Firm 2's industry and p' and Q' denote price and total quantity in Firm 3's industry.

The firms interact as follows. First, Firm 1 chooses between E2 and E3, where 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 chose E2, Firms 1 and 2 compete as Cournot duopolists, where they select quantities q1 and q2. In this case, Firm 3 automatically gets the monopoly profit of 36 in its own industry. On the other hand, if Firm 1 chose E3, then Firms 1 and 3 compete as Cournot duopolists, where they select quantities q1' and q3'. In this case, Firm 2 automatically gets the monopoly profit of 20¼ in its own industry.

Part a Draw the game tree.

Part b Calculate the subgame-perfect Nash equilibrium of this game and report the subgame-perfect equilibrium quantities. In the equilibrium, does Firm 1 enter Firm 2's industry or Firm 3's industry?