For reference, this is discussed on p. 14 in the PHB: "Some spells and class features give you a different way to calculate your AC. If you have multiple features that give you different ways to calculate your AC, you choose which one to use." So a Sorcerer with Draconic Resilience would not benefit at all from Mage Armor.
So, a shield would not stack with Mage Armor but would it with Draconic Resilience?