mind game is a noun meaning "any game designed to exercise the intellect". It carries 2 recorded senses.
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”
“the jeweler's mind game is to convince lovers that the size of a gemstone reflects the depth of their feelings”
Definitions, synonyms and semantic relations for mind game come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.