Two students, X and Y, are given blank cards. Each student is to write a number between 0 and 100. The cards are then collected and the numbers on them averaged. The student whose choice is closest to...

Extracted text: Two students, X and Y, are given blank cards. Each student is to write a number between 0 and 100. The cards are then collected and the numbers on them averaged. The student whose choice is closest to half of the average is the winner. (a) Write down the best response for each player. (b) What is the Nash equilibrium of this game?