Life vs. Life is based on a game first invented in the early 1970's by mathemetician John Conway. In Conway's Life and Life vs. Life the player is presented with a grid of cells. Each cell may be either on or off. After a pattern of live cells is established on the grid they are set to animate and the action proceeds in generations. Every generation each cell checks the eight cells immediately neighboring it to see how many neighbors are alive and reacts according to these four rules.

If a dead cell has exactly three living neighbors it will become alive or is born.
When a live cell has one or zero living neighbors it will die.
A live cell will also die if it is surrounded by four or more living neighbors
Any cell with exactly 2 neighbors will not change states

Life vs. Life adds a couple of rules to Conway's system with the addition of another player. There are two colors of cells in any board competion, red and blue. When the game is activated and the cells start interacting the follow the same basic rules of Life and expand into each others territory. However when the red cells interact with blue cells the resulting cells are either red or blue.

A birthed cell has the color of the majority of the cells around it. 2 blue cells and 1 red cell produce another blue cell.
A live cell surrounded by 2 or 3 cells of the other color is "captured" and changes color. A red cell with two blue neighbors and 0 red neighbors will turn blue.

The other major difference between Conway's set of rules for Life and Life vs. Life is our arena style boards. Conway used an infinite grid but the boards in Life vs. Life are set up to wrap (like pac-man or asteroids) where a cell born outside the boards boundaries will instead be born on the opposite side. For instance a cell born off the right side of the grid will instead appear as the first cell on the left. The same is true for the top and bottom.