A “badger game” is a form of blackmail, employed upon a man of position or wealth who is enticed into a compromising situation by a woman and is then “discovered” by one professing to be her husband.
To avoid disgrace under threat of legal procedure or newspaper publicity the victim is under the thumb of the conniving operators.
To badger, in criminal slang, is to blackmail.
This meaning arose from the cruel sport of badger baiting, practiced from time immemorial until comparatively recent years, in which a live badger was placed in an artificial hole, such as a barrel, and dogs were set upon it.
Thus “to badger” came to mean “to worry, tease, pester,” or, leading to the sense above, “to subject a person in one’s power to persecution; hence, to blackmail.”
This form of blackmail is probably as old as the hills, but association with the term “badger” and the present name of the practice are American innovations of the past hundred years.