First of all, yes, the two players can be in the same cell, even at the beginning of the game. That only means that the first player that arrived there will take its value.
Test:
5
1 2 3 4 5
1 1
Answer:
15 0

Test:
5
1 2 3 4 5
5 5
Answer:
15 0

Secondly, both players play optimally, so it is not a good idea to try and solve this problem using greedy methods. Furthermore, it is not even necessary to try and iterate each move. It suffices to find a technique that applies for each game and then it all reduces to computing a simple sum:) Good luck!