1. [25 points] Consider the following game between Player 1 and Player 2: . Player 1 moves first, chooses between a and b. . Player 2 observes Player 1's choice. . If Player 1 chooses b at the initial decision node, then Player 2 moves to choose between L and R. If Player 2 chooses L, the resulting payoffs will be 3 for Player 1 and 2 for Player 2. If Player 2 chooses R, the resulting payoffs will be 0 for Player 1 and 1 for Player 2. . If Player 1 chooses a at the initial decision node, then Player 1 and Player 2 play a simultaneous- move game where Player 1 chooses between X and Y and Player 2 chooses between W and E. The payoffs for this simultaneous-move game are given by the following payoff matrix: P2 W E X 2, 1 1, 0 P1 Y 0, 0 0, 2 a. Present the entire game in extensive form (draw the game tree). b. Solve for all the subgame perfect equilibria. Denote the equilibria in terms of equilibrium strategies of the players