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.
