Introduction to Game Theory/Battle of the sexes
In this game the players want to cooperate with each other, but they disagree about the best outcome for the game.
Two friends want to meet but disagree on the venue. One prefers to watching boxing while the other prefers ballet. However, if they show up at different sites, they will be unhappy without the other. We can model this game as a two player strategic game:
The table clearly shows that the best choice for the two friends is to both play the same game since neither of them will be happy without the other. The only question left is which game to play.
This game is also known as Bach or Stravinsky. For a modern-day equivalent, let the two choices be the online multi-player game sites EverQuest and Starcraft.