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Other spells/effects than mage armor deal with magical force: Armor of Agathys involves a protective magical force, but looking at the spell it is probably related to the cold counter-damage. Given that imprisonment's other effects all have visible manifestations, we could reasonably conclude that the sphere of magical force created by its ...
The rules for Armor Class state: If you have multiple features that give you different ways to calculate your AC, you choose which one to use. However, these rules are somewhat meta - I cannot articulate what it would mean in-universe for a creature with natural armor to choose to use the bonus from mage armor instead. It might be possible, as ...
Mage Armor says ... a protective magical force surrounds it until the spell ends ... ends if the target dons armor or ... This spell does not give you armor—it gives you a protective magical force—so it has no effect on these abilities. Note that it does not stack with unarmored defence—you get whichever is better.
The spell Mage Armor specifies that. you touch a willing creature. Spells do what they say, so Mage Armor works on a willing creature, with the singular article -- only one target. That said, Mage Armor seems eligible for the Sorcerer metamagic Twinned Spell, which could cause it to target two creatures.
Mage armor gives you an AC calculation method of 13 + Dex mod. The fact that your Dex mod is +3 is just an odd coincidence; if your Dex mod was +0, mage armor would still give you an AC of 13 (before considering any AC bonuses). Moving on to AC bonuses... The Defense fighting style requires armor. The Defense fighting style option states: While ...
Also worth noting is that transforming into a form with natural armor does not cancel out Mage Armor, either. From SRD p.255's description of monster AC: Armor Class. A monster that wears armor or carries a shield has an Armor Class (AC) that takes its armor, shield, and Dexterity into account.
If you cast mage armour on a monk wearing a Ring of Protection and Bracers of Defense, and the monk had Dex 18 and Wis 15, then the monk must choose to use either the mage armour (13+Dex) OR the Unarmoured Defence feature (10+Dex+Wis), but may add both Ring (+1 AC) and Bracers (+2 AC). AC = 20 in this example.
In terms of boosting your own AC, the two features (Draconic Resilience and Mage Armor) will not stack. Each is worded as setting AC to 13+DEX, rather than increasing your AC by 3. (Contrast this with the wording of the previously mentioned Shield spell.) So really, the only point of a draconic sorcerer learning Mage Armor would be buffing ...
Mage armor: You touch a willing creature who isn't wearing armor, and a protective magical force surrounds it until the spell ends. The target's base AC becomes 13 + its Dexterity modifier. The spell ends if the target dons armor or if you dismiss the spell as an action.
5e does not use named bonuses as far as we can tell (preferring Advantage most times other editions would use a named bonus), and really Mage Armor is not a bonus, it's a set amount of AC. The key point on these two spells is that Mage Armor affects your base AC whereas Shield is a bonus to your AC. In this case there is no potential conflict ...