A grid paper game

This game can be played on any size grid, below I show a game on an 8x8 grid. Graph paper works good.  There are 2 players, one player plays the odd numbers and goes first the other plays the even numbers. When it's a players turn they have to play the next number to the left, right, above, or below the last number played on an unoccupied square, and when someone can't make a legal play the other person wins.
 Here's an example game:

Player A played the 1, then Player B played the 2, then Player A the 3, and so on...As Player B played 8 Player A knew that he couldn't play to the right with his 9 because then Player B could put the 10 in the top right square and win because there would be no place to put the 11. When Player A played the 17 Player B knew he couldn't play the 18 below the 17 because then Player A could play the 19 in the bottom right square and win after 2 more moves. After player A played the 23 Player B knew he couldn't play the 24 above the 23 because then Player A could play the 25 to the right and win every possible way the play could continue. After Player B played the 32 Player A saw that no matter what he did he would lose so he resigned.
  So you see the rules are so simple but the strategy and planning ahead can get pretty involved.  I haven't named the game yet, I'd like to hear any suggestions.