WordNet records no synonym and no antonym for round robin. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a tournament in which every contestant plays every other contestant
a letter signed by a number of people
Synonyms, antonyms and the broader and narrower relations for round robin come from Princeton University’s WordNet. Full sources and licences.