I've mentioned this before, but now here is a post further explaining the so-called "Grand Game" --SΣ
Ludus Deorum (Latin: "Game of Gods"), also called the "Grand Game" and the "Great Game", refers to the relations between the PREs and humans. The ultimate goal of Ludus Deorum is unknown, but the PREs will often form and break alliances with one another in order to reach it. Humans are used as the pieces in this game, being manipulated by the PREs as one may manipulate pieces on a chess or checkers board.
Certain PREs do not involve themselves in the game PRE04 "Grandfather" merely acts as an observer, and PRE06 "Empty City" does not actively participate, but rather serves as a neutral meeting ground for the PREs and their Servants.