Advanced Permissions: set permissions for Parent Page's Owner?

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I have a site with pages organized in to a strict hierarchy: There are groups of pages (page type: City) that the composer will write pages (page type: Walk) under. Each walk page the composer publishes has permissions set so that it's editable by the Page Owner. Right now, I have a user group that can edit the City pages.
What approach would I use to make it so that the owner of the City page can edit all the Walks under it, but not the Walks under someone else's City?