"At some moment of time two players can be located in the same cell."
If this occurs, who will take the number in that cell?
If both of them can take,then they can meet at some point and simultaneously take the number.That will maximize their score.

They move in turns, not simultaneously, so even if they end up in one cell one of them (player one) must have stepped there first and therefore he must have taken the points from that cell.

Thanks []zhi(Bozhin Katsarski)