1. (22) Consider the following game: Fi (a) How many subgames are there? (2) (b) Write the game in Normal Form below. (5) (c) What are the subgame perfect equilibria? (10) (d) Find a Nash equilibrium that is not subgame perfect. (5)4. Suppose that we have the following games (21) Player 2 L C R U 7,3 7.4 -1.3 Player 1 M 3, 2 5,-1 0, -1 D 5,3 6, 2 2, x (a) For part (a). let x = 1. What is the set of rationalizable strategies for each player? Make sure to write out your steps. (Hint: Use IDSDS.) (6) (b) For part (b). let x = 3. What is the set of rationalizable strategies for each player ? Make sure to write out your steps. (6) (c) Now let x be some number much that x30. What is the largest value of s for which C weakly dominates but does not strictly dominate It for player 2 given ANY strategy that player I could play? Explain your reasoning. (6) (d) Why might we prefer IDSDS to IDWDS in most cases? When might we like to USC IDWOST (3)