App Store keeps asking for admin password

I periodically get the following dialog box on my MacBook, running OS 10.9.5:

App Store is trying to install Apple-provided software. Type an administrator's name and password to allow this.

I get this dialog even if I don't have the App Store open on my machine. I have turned off all automatic updates in System Preferences. The problem is that I have no idea what this software is--I don't see any such updates in the App store when I open it. My administrator account is distinct from my user account (which doesn't have admin privileges). I can't disable this popup. It drives me nuts and I think it's a stupid design choice that Apple forces this nagware on my system, doesn't provide information about what it wants to do, and then expects me to type in an admin password and trust it. If I press "Cancel," the box goes away until it pops up later--when, I don't know. If I press "Install Software," it again provides zero feedback.

I hate the App Store. Don't keep bugging me about security updates, and don't install them in the background. Let me decide what to do with my system, and when to do it. I don't want notifications. If I could, I would delete the App Store from my computer entirely.

Looked at my console log too. No info.

So, who can tell me what this is, and how to stop it?