Generally, none at all, or at least no more than anyone else at the table.
This depends on the social contract in place at the table in question. But most social contracts are informal, rather than something you actually write out. Most RPG groups are groups of friends or acquaintances that get together to play the game. In that situation, the GM generally ...
No more or less than any other person in the group.
These roles - DM/GM/Keeper or any other 'administrator' - are titles within the game system. Being a Wizard doesn't mean the player can throw Fireballs, and being the DM doesn't convey any special privileges or responsibilities outside the game.