'Guess 2/3 of the average' normal form

Question

I wanted to represent the 'Guess 2/3 of the average' problem in normal form. The rules for this game are below:

• There are two players. Each player names an integer between 1 and 100.

• The player who names the integer closest to two thirds of the average integer gets a reward of 2, the other players get nothing.

• If there is a tie, each player gets reward of 1

Would the normal form simply be this?

Answer 1

No. The rows and columns correspond to strategies, not to results like "correct" or "incorrect". The normal form of this game has $100$ rows and $100$ columns, corresponding to the $100$ different strategies for each player. For instance, the entry corresponding to player $1$ naming $5$ and player $2$ naming $13$ would contain the payoffs $2$ and $0$.