Plugin page with tag sub pages

Not sure if my title is gonna be as specific as it should but i am creating a plugin that displays links that can be tagged. I want to have permalinks like /links/tag. I have thought about creating this with custom post types but im not sure that will meet my needs as i am doing several other things with these as well.

How can i set it up so that when i go to /links/tag/ that it actually loads the links page with a $tag variable to trigger it to only show that tag?