Question

A challenger (Firm 2) is considering entry into the local phone market in the Bay Area. The incumbent (Firm 1), predicts that a price war will result if Firm 2 enters. If Firm 2 stays out, Firm 1 earns monopoly profits valued at $10 million (net present value, or NPV of profits), while Firm 2 earns zero. If Firm 2 enters, it must incur irreversible entry costs of $2 million. If there is a price war, each firm earns $1 million (NPV). Firm 1 always has the option of accommodating entry (i.e., not starting a price war). In such a case, both firms earn $4 million (NPV). Suppose that the timing is such that the Firm 2 first has to choose whether or not to enter the market. Then Firm 1 decides whether to “accommodate entry” or “engage in a price war.”

What is the subgame perfect equilibrium outcome for this sequential game? (Set up a game tree.)

Answer 1

The game tree in the first page shows that firm 2 will make the first move and thats why he has been given two options either to enter the market or not enter the market. Fter his decision firm 1 will make the decision to either accomodate the entry or start a price war with firm 2.

Payoffs:

Firm1 accomodates, firm2 enters = 4,4

Firm1 wars, firm 2 enters = (1,-1). Reason- Initial fixed cost of firm 2 to enter the market = 2 millions and the profit both will make after the price war = 1 million. Therefore, 1-2 = -1.And 1 for the firm 1 as he dosen't have to pay any costs.

Firm2 do not enter = 10,0.

There will be 2 pure strategy equilibriums and after solving through the subgames by the method of backward induction, we see that the only subgame perfect nash equilibrium is (accomodate,enter).