The tragedy of the commons is in fact modeled as a game in the game-theoretic sense. It's called the CC–PP Game: https://en.wikipedia.org/wiki/CC%E2%80%93PP_game.

bob1029 wrote that "You can have 100% of participants operating in a locally-ideal way while still creating problems in aggregate", and the tragedy of the commons is exactly an instance of this. SaltyBackendGuy is right.