That's not standard equipment.
Standard Equipment
Each side starts out with the equipment that they normally and have been shown to consistently carry on them. For example, Daredevil would have his billy-club, but Reed Richards would not have the Ultimate Nullifier.
In a scenario fight, the contestants in whose city/reality the fight takes place are allowed access to any material resources they usually have there or of any team they're active members of, as long as they can reasonably get to them. For example, in a scenario set in the DCU, Green Lantern would have access to equipment in the JLA Watchtower, but not the Titans headquarters.
Beta Ray Bill would not have Scuttlebutt and Batman would not have the Batmobile, unless otherwise noted in the open post.