The arena games, also known as a gladiator contest, gladiatorial game, or gladiatorial match involved gladiators fighting in ceremonial combat, often in an arena for public entertainment. Typically, they were fought during the Roman times on Earth, but were also fought on Vulcan as in the case of kal-if-fee (PRO: "Kobayashi").
In 2268, Communications Officer Nyota Uhura detected a radio transmission of a television news broadcast from the planet 892-IV. Using the viewscreen, the bridge crew watched the taped results of the arena games from the previous night which included amateur fights between petty thieves from the City Prison, followed by a slightly more professional display in which the gladiator Claudius Marcus killed William B. Harrison, the last of the barbarians. After beaming down to the surface of the planet to look for survivors of the destroyed SS Beagle which had gone missing six years before, the landing party was confronted by armed runaway slaves.
They learned that an old Starfleet Academy friend of Captain James T. Kirk was alive, but that he had violated the Prime Directive and became known as Merikus, the First Citizen, Lord of the Games, and was regarded as a butcher. Shortly after, the landing party, along with gladiator Flavius Maximus, was captured and imprisoned. Merikus revealed to Kirk that the crew of the SS Beagle who had adapted to life on the planet were still alive, but those who couldn't adapt had died in the arena. Just as Merikus had ordered his crew into the arena, Kirk was to order his own crew of the USS Enterprise to do the same.
After being threatened by Proconsul Claudius Marcus with the slow executions of both Spock and Doctor Leonard McCoy, Kirk refused to order his crew ashore, which resulted in the two of them instead being forced to fight inside the City Arena on a live media broadcast of Name the Winner. Spock and McCoy's fight against Achilles and Flavius was interrupted after Spock performed a Vulcan neck pinch, which was seen as a foul by the Master of the Games. (TOS: "Bread and Circuses")