What do you call a person who advocates the use, against an enemy, of methods borrowed from that enemy, or applies the same moral standards as the enemy does or otherwise copies the enemy's behavior or techniques?
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Depending on context, the word reciprocity or tit-for-tat is used for that approach, most usually, however, not in a negative sense. An advocate for that could in theory be called a reciprocitist, but it's not a very common usage of that term.
A judo throw uses the opponent's momentum against him.
From Shakespeare's Hamlet, the phrase hoisted by his own petard has entered into common usage.
The meaning is less like using the enemy's techniques against him and more like the enemy being caught with his own techniques.
Fighting fire with fire is another phrase.
Sorry, I don't have any single-word phrases, but perhaps one of these colorful metaphors will do.
The strategy is called 'giving them a dose of their own medicine'. It's assumed that this will be unpleasant rather than restorative. I don't know a term for someone advocating this strategy.