Case Description: Early in the Trojan War, Hector challenged any Greek soldier to single combat. At first the Greeks would have none of it, but eventually a few came forward and Ajax took up the challenge. Hector and Ajax duked it out all day. Though Ajax did manage to wound Hector, neither one could really get the best of the other. In the end, the two decided to call it a draw. They were both so impressed with the other that they gave each other parting gifts. Hector awarded Ajax his sword, and Ajax gave Hector his girdle.
Addendum: Both of these gifts seemed a little cursed. Ajax actually ended up killing himself with Hector's sword, and Hector ended up having his dead body dragged behind Achilles' chariot with Ajax's girdle.