Why does the MacOS App Store ask for other users Apple ID password? We have an iMac with two users A and B who 


are both logged in
are both administrators
have different Apple IDs (and are both logged in to their's)


Today A wanted to update an app using the Updates function in the app Store and was asked for B's password. As usual, the Apple ID was not to change, it just asked for the password.  It was definitely A who first installed this app because B never uses it.  In fact, it is not even on the list of "purchases" of B (it's a free app, though).

What to do about it?

Curious Addendum: A got B to log in and update the app, which worked fine without even asking for B's password or asking to close the app which was running in A's logged in account. Usually, when A updated the app in the past, it would refuse to run an update while the app was running.
Software you buy through the App Store is registered to an Apple ID, not a computer. This gets confusing when multiple people use their Apple ID to install software on the same computer. 

The installers for some applications, often ones that have processes running the the background all the time, are often smart enough to quit and restart as part of the install/update process. 

Hope this helps!
Ric