Two students are to take an exam, and 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 B. Student 1's score equals x1 -1.5, wherex1 is the amount of effort she invests in studying. (That is, I assume that the greater the effort, the higher is the score.) Student 2's score equals x2, where x2 is the amount of effort she exerts. It is implicitly assumed that student 1 is the smarter of the two, 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 x2can take any value in {0,1,2,3,4,5}. The payoff to student iis 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 IDSDS.
b. Derive the strategies that survive the iterative deletion of weakly dominated strategies. (The procedure works the same as the iterative deletion of strictly dominated strategies, except that you eliminate all weakly dominated strategies at each stage.)