184.6. Control of a Battlefield determines Control of its Abilities.
184.6.a. While a Battlefield is Controlled , its Controller controls its Abilities . That player takes responsibility for adding them to the Chain if applicable, and makes all choices required by them unless otherwise specified.
184.6.b. While a Battlefield is Uncontrolled , its Abilities are also Uncontrolled. The Turn Player takes responsibility for adding them to the Chain if applicable, makes all choices required by them unless otherwise specified, and is treated as their Controller if any game rule or effect requires one. Example: The Arena’s Greatest is a battlefield that reads “At the start of each player's first Beginning Phase, that player gains 1 point.” This ability will usually trigger while the battlefield has no controller. If it does, the Turn Player goes through the steps of adding the ability to the chain and receives priority after doing so, exactly as if they controlled the ability.
184.6.c. “You” in a battlefield’s abilities refers to the battlefield’s Controller , as does the implied “you” in instructions like “draw 1.” If the battlefield has no Controller , “you” refers to no one, and all such instructions are ignored.