I am getting the following error when I build my Android App project in Visual studio 2015.
No resource found that matches the given name (at \'value\
Try doing and a clean all and check that ALL the content under the obj has been deleted and then perform a build all.
If that does not work:
I would try removing the ~GooglePlayServices~ nugets/references and re-add just the Xamarin.GooglePlayServices.Mapsnuget which will bring in the ~Basement and ~Base libraries.
You should end up with a generated manifest that only has one reference to google_play_services_version and that resource should be picked up from Debug/android/XXX/YYYYYY/ZZZZZ/R.java:
i.e.
public static final int google_play_services_version=0x7f070000;