Activities that involve the striking of one individual by another are called corporal from the term corporal punishment. Typically corporal activities include spanking, flogging, paddling, and caning.
The use of punishment as an excuse for an erotic encounter. She burnt the toast that morning, forgot to say, ‘Sir,’ or some other trivial misdeed and, alas, must be corrected. Somehow, both end up getting what they crave. As a game, this beats the heck out of strip monopoly. Punishment is an erotic game that should never be used to address serious problems.