Agent 1: Try my best to do it :)
Agent 2: The Converging Agent that likes to make connection

  A B C D E F  
1 . X X X X . 1
2 O . . . . O 2
3 O . . . . O 3
4 O . . . . O 4
5 O . . . . O 5
6 . X X X X . 6
  A B C D E F  

Turn 1: Agent 1 -> B6B4

  A B C D E F  
1 . X X X X . 1
2 O . . . . O 2
3 O . . . . O 3
4 O X . . . O 4
5 O . . . . O 5
6 . . X X X . 6
  A B C D E F  

Turn 2: Agent 2 -> F4D6

  A B C D E F  
1 . X X X X . 1
2 O . . . . O 2
3 O . . . . O 3
4 O X . . . . 4
5 O . . . . O 5
6 . . X O X . 6
  A B C D E F  

Turn 3: Agent 1 -> C6C4

  A B C D E F  
1 . X X X X . 1
2 O . . . . O 2
3 O . . . . O 3
4 O X X . . . 4
5 O . . . . O 5
6 . . . O X . 6
  A B C D E F  

Turn 4: Agent 2 -> A3C3

  A B C D E F  
1 . X X X X . 1
2 O . . . . O 2
3 . . O . . O 3
4 O X X . . . 4
5 O . . . . O 5
6 . . . O X . 6
  A B C D E F  

Turn 5: Agent 1 -> E6B3

  A B C D E F  
1 . X X X X . 1
2 O . . . . O 2
3 . X O . . O 3
4 O X X . . . 4
5 O . . . . O 5
6 . . . O . . 6
  A B C D E F  

Turn 6: Agent 2 -> F2D2

  A B C D E F  
1 . X X X X . 1
2 O . . O . . 2
3 . X O . . O 3
4 O X X . . . 4
5 O . . . . O 5
6 . . . O . . 6
  A B C D E F  

Turn 7: Agent 1 -> B1D3

  A B C D E F  
1 . . X X X . 1
2 O . . O . . 2
3 . X O X . O 3
4 O X X . . . 4
5 O . . . . O 5
6 . . . O . . 6
  A B C D E F  

Turn 8: Agent 2 -> A5C5

  A B C D E F  
1 . . X X X . 1
2 O . . O . . 2
3 . X O X . O 3
4 O X X . . . 4
5 . . O . . O 5
6 . . . O . . 6
  A B C D E F  

Turn 9: Agent 1 -> E1E2

  A B C D E F  
1 . . X X . . 1
2 O . . O X . 2
3 . X O X . O 3
4 O X X . . . 4
5 . . O . . O 5
6 . . . O . . 6
  A B C D E F  

Agent 1 wins!