Find the pure strategy Nash equilibrium, sub-game perfect Nash equilibrium and perfect bayesian equilibrium of the given game.

E P1 (1,0,0) D P2 X Y P3 L R L R (2,2,2) (0,1,0) (2,0,0) (2,0,0) (a) Compute the Nash Equilibrium in pure strategies of the game above. (4 points) (b) Compute the subgame perfect Nash equilibrium. (2 points) (c) Compute the perfect Bayesian euilibrium. (4 points)