Do not feel like typing a lot of words,I am going to type the main points.
For a room with 2 players,you usually have to compete for monsters.
The more area you can control,the more likely you can kill it before the other one does.
Assumptions:
Both players has same speed
They can only kill monsters when they "touch" it
There is no attack delay
Terrain ignored
The spawn origins of monsters are evenly distributed
For a given range,such as a to b.
a-----------------------------------b
c is a player and d is another player.
Deploy c.
a------------c---------------------b
Domain of c:a to c and c to b(=100%)
Deploy d.
a-----------c----------d----------b
Domain of c:a to (c+d)/2
Domain of d:(c+d)/2 to b
As you can see,to increase your domain,you have to go closer to the other player so the interval between one end and the half of total distance between you two increases.
Eventually,both players will have zero distance between them and they meet at the middle point((a+b)/2).
At this moment,
Domain of c:a to (a+b)/2=50%
Domain of b:(a+b)/2 to b=50%
It seems that it is back to the basis.
However,the average distance they have to travel to kill a monster increases.
For a fixed speed,time needed is directly proportional to distance.
Therefore,average time needed to kill a monster increases.
When both players pursue their own interest,neither of them will gain.
Yet if only one player does this,he is most likely to dominate the room.