Let's consider the following two player game

The parameter Q is an element of {−1, 1} for this game matrix is known only to player

2. 1st player He believes that the probability of Q = −1 and Q = 1 is equal and 1/2. Everything above is common knowledge.

(a) Formally describe this game as a Bayesian game.

(b) Find the Bayesian Nash equilibrium.

(c) What would be all the Nash equilibria of this game if Q=−1 or Q=1 were common knowledge?
 

X 1 Y Y Z L 3,0 2,20 2,20 0,0 2 R 0,0 2,0 3,-0