I have three models in a Rails application: Game represents an instance of a game being played. Player represents an instance of a participant in a game. User represents a registered person who can participate in games.

Each Game can have many Players, and each User can have many Players (a single person can participate in multiple games at once); but each Player is in precisely one Game, and represents precisely one User. Hence, my relationships are as follows at present.

class Game
  has_many :players
end

class User
  has_many :players
end

class Player
  belongs_to :game
  belongs_to :user
end

... where naturally the players table has game_id and user_id columns, but games and users have no foreign keys.

I would also like to represent the fact that each Game has many Users playing in it; and each User has many Games in which they are playing. How do I do this? Is it enough to add

class Game
  has_many :users, :through => :players
end

class User
  has_many :games, :through => :players
end