[ Bayesian Game - reposting this question because the answer I received from the previous question was not correct; questions were not answer].
Consider the following Bayesian Game:
1 \ 2 A B
A 0, 0 θ1 , 3
B 3, θ2 2, 2
The value of θ1 ( i = 1, 2 ) is private information of player i. For each i, the value of θ1 is either 0 or 6. The state of the world (θ1, θ2) is drawn from the following contribution.
θ1 \ θ2 0 6
0 1/8 1/2
6 1/4 1/8
Please enumerate player 1’s pure strategies.
Suppose that player 1 observes his own type θ1 = 6. What is the probability distribution of θ2 for player 1? Show your solution.
Suppose that player 2 observes his own type θ2 = 6. What is the probability distribution of θ1 for player 2. Show your solution.
Verify that si = VA ( Si (0) = B, Si (6) = A) for each i = 1, 2 is Bayesian Nash equilibrium of this game. Also, show that this is a unique (pure strategy) Bayesian Nash Equilibrium. Show your solution.