parallels 13, high sierra, clicking allow does nothing

I recently upgraded to a new iMac, which came with High Sierrra. When I tried to launch Parallels Desktop 12.2, I got a message that I needed to go into the System Security Prefs and click allow. Clicking did nothing, even after unlocking the pane.

I upgraded to Parallels Desktop 13.2 ($50), and I get a similar message. Clicking "Allow" still does nothing. I looked in the Console to see if there was anything to be gleaned there, but there didn't seem much of interest, except maybe this:

Kext rejected due to system policy: <OSKext 0x7f9aac667f70 [0x7fff995f6980]> { URL = "file:///Library/StagedExtensions/Applications/Parallels%20Desktop.app/Contents /Library/Extensions/10.9/prl_hypervisor.kext/", ID = "com.parallels.kext.hypervisor" }

and this:

com.parallels.kext.hypervisor failed security checks; failing.

I'd appreciate some help with this. Though I don't use Windows a lot, there are certain applications I can't do without.