Copyright (c) 1972 Colin Vout

This game is played on an empty NxN square board (say 8x8):

MOVE - A Black stone moves one cell right, up or down. A White stone moves one cell up, left or right. That cell must be empty. There are no captures.
Black stones leave the board by moving onto the right edge. White stones leave the board by moving onto the up edge.
GOAL - Wins the player who made the last move. However, a player looses if he stalemates the opponent! 

An example

White moves to cell [1], Black is forced to move f7-f8. If White moves f6-f7 he looses (because Black is stalemated).

But, if White moves h8 off board, then Black moves g8-h8, g7-g8, h8 off-board, g8 off-board, f8-g8, g6-g7 and White because Black has run out of options (f6 and g7 forbid the White stone to move down).

Herein is a CGI webpage that plays the game. Dodgem is described in volume 2 of Winning Ways for Your mathematical plays, where the 3x3 version is completely analyzed (1st player wins). For 4x4 and 5x5 boards, the game is a draw. Also, ZIllions package includes dodgem. There is another variant called Dodge This!.