Consider the following Bayesian game. Nature chooses between the states x and x' where x is chosen with a probability p. Player 1 observes the state but player 2 has no information regarding nature's choice. Player 2 believes that with probability p he is in state x. The two players then play a simultaneous game with payoffs given below. Player 1 chooses between T and B and Player 2 chooses between L and R.

1\2 L R

T 12,9 3,6

B 6,0 6,9

1\2 L R

T 0,9 3,6

B 0,0 6,9

State xState x'

1. Write down the elements of a Bayes Nash Equilibrium.
2. Solve for a pure strategy Bayesian equilibrium (ia) when p=2/3
3. Solve for a pure strategy Bayesian equilibrium (ia) when p=1/3