“The Game” is episode fifteen of season three of Stargate: Atlantis.
A planet is found that has a number of Ancient satellites in geosynchronous satellites. One of the countries on the planet has a flag bearing Rodney McKay’s face, a flag he designed for a game that he and Colonel Sheppard were playing on Atlantis.
The game seemed to be one like The Settlers or Civilization, only more advanced, allowing the players to run two different countries and attempt to develop them. Only it was not a game.
Sheppard and McKay have unwittingly brought two countries to the brink of war, and have to figure out how to find a peaceful solution. Which isn’t easy, as they have raised tensions to a serious level.
A moral dilemma posed by Rodney at the beginning of the episode rather crudely introduces the concept that the episode explores. Another episode that has no bearing on the Wraith plot, and one with an easy to spot ending.