/usr/share/mate/applications/ is in ubuntu-mate-default-settings 18.04.17.
This file is owned by root:root, with mode 0o755.
..
/usr/share/mate/applications/compton.desktop
/usr/share/mate/applications/debian-uxterm.desktop
/usr/share/mate/applications/debian-xterm.desktop
/usr/share/mate/applications/defaults.list
/usr/share/mate/applications/display-im6.desktop
/usr/share/mate/applications/display-im6.q16.desktop
/usr/share/mate/applications/gnome-language-selector.desktop
/usr/share/mate/applications/gtkhash.desktop
/usr/share/mate/applications/kde-Kantiword-Installer.desktop
/usr/share/mate/applications/org.mate-desktop.mate-eiciel.desktop
/usr/share/mate/applications/software-properties-gtk.desktop
/usr/share/mate/applications/tilda.desktop