@Maurits
That is not really true. While people obviously refer to any important matchup as "the big game", that is not used as a name for the game in the way it is for Cal-Stanford. The UW-WSU game is called the Apple Cup. The USC-UCLA game is occasionally referred to as the Battle for LA or Crosstown Battle, but is usually just called the USC-UCLA game. Other games that have names include Florida-Georgia, "The world's largest outdoor cocktail party" (commonly shortened to The cocktail party"); Harvard-Yale, "The Game"; Georgia-Georgia Tech "Clean Old-fashioned hat"; Utah-BYU, "The Holy War"; etc.