Please explain how to solve part 1 till 5 with explanation

Two people are working as a team on a diicnlt problem set. Due to the deadline and the diioulty of the problem set, if two people both work on the problem Set they can nish in time and get points, but as long as at least one person secretly shirks and does not work, the problem set won't be nished in time and both will get mm grades. Also, working on the problem set causes stress and decreases happiness so the payo' matrix looks like below, where h is how much each player dislikes working [I] 1': h 5 10). m -1m- Not wk mm 1. Find all pure strategy equilibria of this game and exprms as a function of h. 2. Find all mixed strategy equilibria of this game and exprem as a function of h. 3. Does the increase of it (increase in how much students hate working) make probability of 'work' higher in mixed equilibrium? Explain briey. 4. Now, assume that not all the problem set gets graded, and this particular problem set gets graded with a chance of c {G 5 h S 10, and 5 10 h}. In this case, the payc' matrix will change: Find all mixed strategy equilibria as a function of c and h. __ 5. (continued from 4) Since the professor wants all students to work on all problem sets, he is considering what the optimal level of c will he. Does the increase of c make the probability of 'work' higher in mixed equibrium? Explain the intuition briey