Single Combat, the idea of two champions solving a dispute or battle on behalf of their group, is a meme that has deep seated roots in the human psyche. As with many pervasive mythic ideas, it is an elaborate piece of wishful thinking with some foundation in real events.

Probably the single most famous single combat is the bible story of David and Goliath. it displays many of the themes that run through most stories about single combat in mythology: two forces facing each other with the assurance of a bloody battle that will profit neither side, champions chosen by each side to fight to the death, the underlying implication that the combat only serves as a medium for the gods, fate, whatever, to decide the outcome, and the presence of an element of magic, information, technology, whatever, that gives one side the upper hand. The famous slingshot slays Goliath and the Philistines flee in a demoralized state. David not only wins the battle and the war for the Hebrews, but even becomes King.

Tom Wolfe in The Right Stuff compellingly makes the case that the Cold War race to space was a modern rebirth of the single combat:

During the Cold War period small-scale (compared to global thermonuclear war, everything else is small potatoes)competitions once again took on the magical aura of a "testing of fate," of a fateful prediction of what would inevitably happen if total nuclear war did take place.
and it is the astronauts that do hand to hand combat as they strive to reach each space milestone. They represent the best that each side has to offer in terms of technology and courage. It is this concept of the "testing of fate" that recurs again and again. It is found in the Star Trek TOS episode 19 Arena where Kirk and a cheesy alien reptile, the gorn fight for the continued existence of their respective races. This is the wishful thinking part, as the old saying says that there would be no wars if the only way to fight them would be to have the leaders of each warring faction strip naked in an arena and pelt each other to death with socks filled with horse manure.

Though there are some isolated cases were battles were decided by single combat, in most cases it only served as a preamble to all out combat.

Tom Wolfe, The Right Stuff , p. 97