Your professor lost two homework assignments, one which was yours and one which belonged to one of your classmates. Your professor remembers that the grade was the same on both assignments, but doesn't remember what it was. The students know the true grade because they have checked the answer key, and determined which problems they answered correctly and which problems they missed. The professor devises the following plan. Each student can tell the professor a grade between 0 and 100 (integers only). If both students write down the same number, then the professor will take that as the true value, and each student will be assigned that grade. If the students write down different numbers, then the professor takes the lower number to be the true grade (call it TG) and then gives a grade of TG 2 to the student that reported the high grade(because they may have been lying to increase their grade) and a grade of TG+2 to the student that reported the lower grade (because they were being more. a) Assume that players can only choose either 5 or 10 for their grades. Write down the game in the normal form, determine which game this is, and find the Nash equilibrium. b) Assume that players can only choose either 9 or 10 for their grades. Write down the game in the normal form, determine which game this is, and find the Nash equilibrium. c) Now assume that players can choose any integer between (and including) 0 and 100.What is the Nash equilibrium?