Redirect Without Changing URI

Hi all,

I recently ran into a situation where I had several pages that had the 
same content, but represented different states in the application due to 
where links from the page pointed. As an example, consider a game where 
you move from room to room, each room may have monsters to fight or 
items to pick up and may have any number of exits. You might have two 
rooms with the same contents and the same exits, but exiting north from 
the first room brings you to a different place than exiting north from 
the second.  My first thought on representing this would be to have each 
exit be a hyperlink with a relative URI, and respond to the request to 
get one of the identical rooms with a protocol-level redirect (to the 
same shared resource) that doesn't cause the client to change the 
meaning of relative URIs. Do any REST-capable protocols (the only one I 
know of is HTTP?) support this? Could they?

Thanks,
Shea