Antagonistic game (Zero-sum game)

The first player is colonel Blotto. He has 2 battalions. His opponent has 3 battalions. There are two fields they are fighting over. Blotto and his opponent could move in any number of available battalions to any of two fields. Points, that a player gets from one field are calculated as follows: player gets as many points as the number of battalions of an opponent at every field plus one if an opponent has fewer battalions and zero points if players send an equal number of battalions to the field.

For example, if Blotto sends 2 battalions to one of the fields and his opponent sends 2 battalions to the same field, then on that field it would be a draw. On the other field Blotto would have 0 battalions and his opponent would have 1 battalion, so Blotto's opponent wins 1 points there (0 Blotto's battalion + 1 additional point) and Blotto loses 1 points. The final result would be -1 points for Blotto.

We will denote the number of battalions, that a player sent to the fields by a tuple $(a, b)$. Here $a$ is the number of battalions sent to the first field and $b$ is the number of battalions sent to the second field. Fill in the payoff matrix of the game:

Give an answer using the following template:

0 -1 0 0

0 0 0 0

0 0 -1 0