Consider the following incomplete information game between Firm 1 (potential entrant) and Firm 2 (incumbent). Firm 1 has undertaken an R&D project for developing a new product. The outcome of the project is uncertain and private information of Firm 1. The new product is good with probability p and bad with probability 1-p. After learning the quality of the product, Firm 1 decides whether or not to enter the market. If Firm 1 does not enter, the payoffs are (0,4) (Firm 1 gets 0 and Firm 2 gets 4). If Firm 1 enters, payoffs depend on the quality of the product and the response of Firm 2. Firm 2 can start a price war (F-fight) or can accommodate the entry (A-accommodate). If the product is good, F leads to payoffs of (1,-2) while A generates payoffs of (2,-1). If the product is bad, F leads to payoffs of (-1,2) while A generates payoffs of (1,1).
This game has a pooling equilibrium in which Firm 1 always enters (with a good and a bad product) if p>= x, where:Option 1 : 2/3Option 2: 1/2
Option 3: 3/2
Option 4: 1/4
Provide step by step explanation