Bullying does escalate. Therefore, teaching your kid to escalate on their side as well just makes it happen faster. The solution to escalating warfare is to break the cycle.
Bullying is typified by a victim being picked-on mercilessly because he never fights back. Because the bullying tears him down. Because the bullied is a victim.
Bullying isn't a contest for the bully. They do it precisely because it isn't. They're not trying to 'win', they're trying to make someone else feel as bad as they feel. If they can't do that, because the victim refuses to be victimized, they find a new victim or find a new outlet.
If your kid just gives the bully a few bruises but ultimately loses the fight then they've sent the message that they're not an easy target, and the bully has saved face.
That is not true. MAD worked in the cold war. The solution is to let the other side know you will not go gentle into that good night.