If they were beaten, they adopt a combination that would have beaten the opponent. The psychology of game-players in PVP games suggests that they would much prefer to use a different set of equipment rather than copy a set of equipment someone used against them.
Goodness, thank you! I had that correct in my first comment on this whole post, as I played an MMO called Guild Wars avidly for a while. I apparently forgot that here. It does make the simulation somewhat more challenging to model.
Note: this image does not belong to me; I found it on 4chan. It presents an interesting exercise, though, so I'm posting it here for the enjoyment of the Less Wrong community.
For the sake of this thought experiment, assume that all characters have the same amount of HP, which is sufficiently large that random effects can be treated as being equal to their expected values. There are no NPC monsters, critical hits, or other mechanics; gameplay consists of two PCs getting into a duel, and fighting until one or the other loses. The winner is fully healed afterwards.
Which sword and armor combination do you choose, and why?