Here's what rhymes with hypergame.
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gain cane main pain chain grain rain reign attain ln vain vein lane sane crane fain lain pane pertain rein bane mane tain vane wane arcane deign feign germane skein urbane arraign thane wain brain obtain domain plain plane train drain slain stain cocaine regain terrain detain hurricane sugarcane twain certaine inane moraine appertain swain chicane murrain contain remain campaign strain retain sustain ascertain entertain insane champagne disdain profane abstain mundane ordain butane cellophane overlain romaine sprain urethane ingrain reattain explain maintain complain refrain humane aeroplane halothane humaine coxswain retrain hydroplane wholegrain restrain constrain monoplane legerdemain windowpane preordain inhumane polyurethane demimondaine foreordain reexplain raceme