When you have both someones, you have both people. You'll notice over time that 者 is often used to indicate a person or type of person, so keep that in mind for future words as well!
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
Both people's thoughts are not the same.
With the power of both people, I think you can reach the right answer.
In the all US tournament, it was a draw for both sides with the same score.