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Achilles's didn't know it, but he was also in desperate need of the exchange, because his constant failure to deface the body just reminded him of his dear friend Patroclus. In order for him to mourn Patroclus, he has to understand that the family on the other side of the war was feeling the same emotions. In other words, the communion with the enemy granted him freedom from his agony. In that way, both parties got something important. And obviously, Achilles's is even more rich than he was before from all the king's gifts.