PROBLEM 2 Three classmates, Arthur, Isaac, and Ray are going to take an exam. Each of them is deciding whether to put in effort or to slack. Their grade on the exam depends not only on how well they do, but also on their performance relative to the other students. The grades they will obtain, which depend on how many of the students choose each of the two actions, are shown in the following table: lElutcome Grade for hard workerls} Grade for slackerls) 3 students put in 9 art 2 students put in effort, 1 student slacks 1 student puts in effort, 2 students stock 3 students stock Suppose the enjoyment levels from receiving an A, B. or C are represented by mo. and c, respectively. Suppose also that if a student puts in effort, it reduces his enjoyment by 4, no matter the grade he gets. TASKSIQUESTIDNS 2.1 Fill in all players' payoffs in the following table (rewrite the table on your assignment submission} using the letters provided above and the [dis] enjoyment value of effort. Three values have already been filled in, as an example. Strategy Combinations \"\"Wm} {effort effort, slack} ( g . ) {\"\"'ef'r'mm {stat-e effort, slack} {sauce slack, effort} [siesta slack, slack} r l l I L 2.2 In order for the strategy combination {effort, effort, effort} to be a Nash Equilibrium, it is necessary that b - 4 2 c, and to be a Strict Nash Equilibrium, it is necessary that b - 4 > c. Why? 2.3 If b -4 = c, the strategy combinations {effort, effort, slack}, {effort, slack, effort}, and {slack, effort, effort] will all be Nash Equilibriums. Why? 2.4 Two of the following 4 conditions must be true for {effort, slack, slack}, {slack, effort, slack}, and {slack, slack, effort} to be Strict Nash Equilibriums. Identify them, and explain your answer: Condition 1: a - 4 > b Condition 2: a - 4 c Condition 4: b - 4