Subduing in 1st Edition
In AD&D (1st Edition), the rules for subduing a dragon were found in the Monster Manual I, under the DRAGON entry:
Subduing a Dragon: An attack on a dragon to subdue, and thus capture it may be opted for if such intent is announced in advance of the combat. Silver, gold, chromatic and platinum dragons cannot be subdued. (Monster Manual, 1st Edition, p. 30)
It is worth noting that in that edition, "chromatic" wasn't the generic name for evil (and coloured) dragons, but the name of Tiamat, the 5-headed dragon, ruler and mother of all evil drakonkind.
The mechanic was then described :
- All points of damage scored by attacks upon the dragon are considered non-fatal.
- The total number of HP scored each round is stated as a percentage,
ratioed over the HP the dragon had at the start of combat
(i.e. 10 damage done to an adult Black dragon with 40 max HP give a
25% chance to subdue the creature on that particular round).
Then the page goes on with details on the maximum number of attackers possible given the size of the dragon, the value of a subdued dragon in a city and the length of subdual.
Yes, 1st Edition dragons had much fewer HPs than they have in 5e! But so did the PCs...
Subduing in 5th Edition
In 5e, subduing a dragon seems much harder, if even possible.
First, the very nature of dragons (Creatures of ego) make them tough customers for subdual :
Trying to humble a chromatic dragon is like trying to convince the wind to stop blowing. (Monster Manual, 5th Edition, p. 86)
Second, every type of dragon has a distinctive relationship with power, hierarchy and slavery. It's up to the DM to decide if any endeavour of subdual is bound to succeed or fail. Sometimes, guidelines are given in the description of a specific dragon.
For example, Black dragons usually fight to the death if they can't escape :
On the verge of defeat, a black dragon does anything it can to save itself, but it accepts death before allowing any other creature to claim mastery over it. (Monster Manual, 5th Edition, p. 89)
Green dragons are more subtle :
Any creature foolish enough to attempt to subdue a green dragon eventually realizes that the creature is only pretending to serve while it assesses its would-be master. (Monster Manual, 5th Edition, p. 95)
White dragons, finally, seem the most prone to subdual, but only by powerful creatures (which is open to interpretation), and there are consequences:
Powerful creatures can sometimes gain a white dragon's obedience through a demonstration of physical or magical might. Frost giants challenge white dragons to prove their own strength and improve their status in their clans, and their cracked bones litter many a white dragon's lair. However, a white dragon defeated by a frost giant often becomes its servant, accepting the mastery of a superior creature in exchange for asserting its own domination over the other creatures that serve or oppose the giant. (Monster Manual, 5th Edition, p. 102)
TL;DR : there is no proper subdual mechanic in 5th Edition. Dragons are hard to enthrall, due to their ego. DM must assess the reaction of each dragon, based on it's type and characteristics, which are given in the Monster Manual.