Two Player Variations of Life
 There are a number of two player variations on Conway's Game of Life.
Turn-based game. Start from a configuration. On a player's turn, he or she must kill one enemy cell and must change one empty cell to a cell of their own color. Compute next generation. Compete for N turns. [Source: Cornell blog]
Turn-based game. Each player places 40 pieces. Run for 500 generations. [Source: hackerrank]
Turn-based game on a 5x5 board. Each player secretly places 3 pieces. Then they alternate turns. Place a new piece and run next generation. Game continues until no more live pieces. [Source: Life for Two]
Players gain points for going across the opponent's side. The players have the ability to continuously create live cells within their starting-area. [Similar to this game: Game of Bigotry]
Game of Life and Death [Source: https://www.youtube.com/watch?time_continue=374&v=JkGZ2Hl1l8c] This one has rules similar to the Cornell game for two people. It's in the iphone App Store.
Another two person game. This one includes some randomness when both white and black have three neighbors. [Source: p2Life]
Multiplayer Game of Life [Source: lifecompetes.com]
References
https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life - Wikipedia article on Game of Life
https://www.atariarchives.org/basicgames/showpage.php?page=102 - Life for Two
https://forums.tigsource.com/index.php?topic=1895.0 - Game of Bigotry
https://arxiv.org/pdf/cond-mat/0207679.pdf - p2Life
http://lifecompetes.com/ - multiplayer