That stinks. Lol. Unarmored Defense says "if you're not wearing armor" so Mage Armor should work. Oh well. Thanks for the reply.
If we want to be formal about it - you are still using your Unarmoured Defence - it's an Ac calculation method that calculates your AC as being "10 + Dex-mod + Con-mod". That is the calculation and that is what unarmoured defence does; 10 plus dex plus con.
Mage armour (despite Larian's bad tooltips) is an AC calculation method that calculates your AC as being "13 + Dex-mod". That is the calculation, and that is what Mage armour does.
(Larian's tooltips used to say 'increases Ac by 3' which was outright incorrect, and the'ye now been changed to say 'sets base ac to 13' which is still not correct, and still misleading...)
A nude barbarian with mage armour cast on them has both effects active - that is to say, neither of them has been negated or disallowed, both are valid in this situation and they may choose to use either method to calculate their AC; they do not have any other special third method of calculating their AC, however - there is no "13 + Dex + Con" method; that doesn't exist.
So, if your barbarian with 18/18 had mage armour on them, they would naturally choose to use their unarmoured defence trait - and calculate their AC as 10 + 4 + 4 = 18, rather than Mage Armour, which would be 13 + 4 = 17.... however, if that Barbarian, during the day, got hit by some effect that suddenly sapped their Con temporarily, and reduced it to 10, their unarmoured defence calculation would now leave them at 10 + 4 + 0 = 14, while their mage armour, which is still active, would let them have 13 + 4 = 17... so the barbarian would use the Mage Armour method to calculate their AC until their Constitution recovered.
The video game attempts to do all of this for you, and uses the highest Ac value that you have access to, out of all of the methods you have available for calculating your AC