There are two posibilities.
1) No one will make a challenge - The trophy is staying in it's position, neutral.
2) One team will start a challenge, a game with a competitor. The between trophy is staying to the team that has won the last game before the time ends.

You must spot which is your main competitor, the most active, and wait to play with him the last minutes of the day.
It's not worthy to spend tokens for extra challenge at the end of the day, because rewards are very poor.