4. Consider the simultaneous-move game represented by the following matrix: Row Player Column Player L R T 2, 0 1, 3 B 1, 1 3, 0 a) If the L0 action places an equal probability on each pure strategy, derive actions for L1 through L4 of each player. b) If all players are level k > 0 reasoners, does it always pay to think more deeply? That is: do players always do better when they have a higher level of reasoning than they would if they had a lower level of reasoning? If not, show with an example. c) The unique Nash equilibrium in this game is in mixed strategies: Row plays T with probability 1 4 and B with probability 3 4 , and Column plays L with probability 2 3 and R with probability 1 3 . Say that the population was made up of a fraction α of L3 players and a fraction (1−α) of L4 players. Are there any values of α such that both players are better off (on average) than they would have been in the unique Nash equilibrium? If so, which?