With the Game API, you can obtain the fantasy game related information, like the fantasy game name, the Yahoo! game code, and season.
To refer to a Game resource, you'll need to provide a game_key, which will either be a game_id or game_code. The game_id is a unique ID identifying a given fantasy game for a given season. A game_code generally identifies a game, independent of season, and, when used as a game_key, will typically return the current season of that game. For instance, the game_code for the Free NFL game is nfl; using nfl as your game_key during the 2014 season would be the same as providing the game_id for the 2014 season of the NFL game (331). As of the 2010 seasons, the Plus and Free games have been combined into a single code. If you always want the current season of a game, the game_code should be used as a game_key.
You can find a list of common game_ids in the official Yahoo! Fantasy Sports documentation for the game resource.