The authorial privilege is the right to decide and narrate events in the game. It is primarily a game framework, supported by the social dynamics of the group. It may be mediated through game mechanics.
Authorial privilege can be handled in a number of ways.
This is the most traditional. The GM has the authorial privilege to describe any events in the game world. However, that privilege is shared to the extent the events must be acceptable. Players have the authorial privilege over their characters' actions. The game design and party creation are shared.
The GM has the only authorial privilege. Players may request to take certain actions.
Rather than a traditional GM or narrator, narration is shared among two or more players. This may be done by consensus, unanimity, dividing up different domains of the game, or taking turns. It may also be built into the game; for instance, players may be given authorial privilege over events through a generous pool of points they can spend to specify a particular event, or players may be required to narrate certain events. For instance, a GM might say, "You visit the tavern. Tell me what transpires there."
Sometimes, authorial privilege is delegated through the system. While one or more players retain their original privilege, the rules may dictate certain things as game reality.
Sometimes players are granted the ability to narrate. For instance, an action point might allow a player to specify a certain item or situation is available. As another example, a PC might have special contacts which they can call on; when the player makes the decision to activate those contacts, they become available. In reverse to the usual situation, the player is the author and the GM merely assents to the proposed narration.
Sometimes, some authorial decisions are left to the game. For example, in some games, characters may have particular traits related to their personality, such as a virtue or vice. The game has provisions specifying how that trait controls the PC, irrespective of what the player might wish. Many GM tasks are delegated this way in most game systems; for instance, a game might specify what a character gains from a period of study.
Sometimes, a game design invites a player to narrate. For instance, in some games, players can propose stunts they would like their character to attempt. The GM assents if the proposed action is permissible. This is an implicit part of any role-playing game; the GM can always choose to accept a player's proposed narration. In a distributed game, this form of delegation is extremely common as players collaborately narrate.