WordNet records no synonym and no antonym for mind game. 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.
any game designed to exercise the intellect
deliberate actions of calculated psychological manipulation intended to intimidate or confuse (usually for competitive advantage)
“football players try to play mind games with the opposition”
Synonyms, antonyms and the broader and narrower relations for mind game come from Princeton University’s WordNet. Full sources and licences.