Two people are to take a test and the professor has instructed them that the student with the higher score will receive

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Two people are to take a test and the professor has
instructed them that the student with the higher score will receive
a grade of A and the person with the lowest score will receive a B.
Student 1ʼs score equals
x1 + 1.5 where x1 is
the amount of effort that she invests in studying. Student 2ʼs
score
equals x2 where x2 is the
amount of effort that she invests in studying. (Implicitly it is
assumed that student 1 is smarter.)
Assume x1 and x2 can take
any value in [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 for
i = 1 and 2.
1. Depict a normal form of the game
2. Derive the strategies that survive the iterative deletion
of strictly dominated strategies.
3. Derive a Nash Equilibrium.