In case of high type, if entrant chooses to enter or stay out ,incumbent Won't build as it follows a dominant strategy in not bulding. And if the incumbent doesn't build, entrant enters
In case of low cost type, the incumber builds irrespective of the entrant enterning or staying out as building is the dominant strategy. And if the incumbent builds, entrant stays out
If p is the probability of high type, then for the incumbent, pay off is
2p+(1-p)*5=2p+5-5p=5-3p and the maximum is achived When p=0, i.e. in the case of low cost type where the incumbent chooses to build
Hence the Bayesian Nash equilibrium is (enters, stays out, builds)
Find the Bayesian-Nash Equilibrium for the following "Entry game?",
Two firms in same product market.
Incumbent chooses Build (B) or Don't Build(D) capacity.
θh=high cost type,and θl low cost type. θh has a higher capacity cost than θl.
Prior probability of θh is p.
Idea is incument earns a higher profit if entrant stays out. So may want to build capacity to threaten a price war and deter entry.
Payoffs are as fallows:
Entrant Entrant
E S E
S
Incumbent B 0,-1 2,0 B 3,-1 5,0
D 2,1 3,0 D 2,1 3,0
Payoffs if θh Payoffs if
θl
a) What is the Bayesian-Nash equlibrium? Describe it based on the value of p1, Which denotes the common prior probability that Entrant's cost is high ( θ).
(NOTE: A Bayesian Nash equilibrium is described by a strategy for the θh type, a strategy for θl type, and strategy for the Incumbent.)
3. Find the Bayesian-Nash Equilibrium for the following Entry game." Two firms in same product market Incumbent cho...
There are two incumbent firms, F1,F2 and also a potential entrant, F3. The steps of the game are: 1. F1 and F2 simultaneously choose outputs q1 ∈ R+ and q2 ∈ R+ respectively. 2. F3 observes q1, q2 and then chooses whether to enter the industry. If she does not, then q3 = 0 and she gets a payoff of zero, but. . . 3. if she has entered the industry, F3 chooses her own output level, q3 ∈ R+....