Two students are to take an exam, an the professor has instructed them that the student with the higher score will receive a grade of A and the one with the lower score will receive a grade of B. Student 1's score equals x1 + 1.5, where x1 is the amount of efforts she invests in studying. Student 2's score equals x2, where x2 is the amount of effort she exerts. It is implicitly assumed that student 1 is smarter than student 2, in that, if the amount of effort is held fixed, student 1 has a higher score by an amount of 1.5. Assume that x1 and x2 can take any value (0,1,2,3,4,5). The payoff to student i is 10 - xi if she gets an A and 8 - xi if she gets a B, i = 1, 2.
a) Derive the strategies that survive the iterative deletion of strictly dominated strategies.