The Misplaced Assignments

Rowmeo and Columna are two game theory students whose assignments have been misplaced. It is known that the students turned in the assignment. The professor tells the students that they have actually scored the same number of points on all assignments so far this semester. He takes them into separate rooms so that they cannot communicate with each other and explains that each student will be given a piece of paper on which to write integer no less than 2 and no more than 9. He also tells them that if they write the same number, he will treat that as the true score and both students will be given that score.

However, if one student writes down a smaller number than the other, then the smaller number will be taken as the true score and both players will be given that score with a modication: 2 extra points will be given to the student who wrote down the lower score and 2 points will be deducted for the student who wrote the higher score.

a) What is the NE number that each student will write?

b) How did you determine your answer?