3. [20 points] Consider a game with 2 players, PI and P2, as depicted in the graph on the next page. First, P1 chooses between L and R, each of these two options followed by a strategic game between the two players. Note that mixed strategies are not allowed in the subgame following L, but are allowed in the one following R. (a) Identify the strategies of each player. (b) Find all pure-strategy Nash equilibria for the subgame following L. Page 3 of 4 pages (c) Find all mix-strategy Nash equilibria for the subgame following R. (d) Find all subgame perfect, equilibria. PI L R P2 P2 (q) L C L C T P1 1, 1 0, -2 T P1 (p) 2, 1 0, 0 M -2, 0 -1, -1 M 0, 0 1, 2