Several newer family games are built entirely around the mechanic of "sanctioned cheating" or investigation: Detecteam Family: Cheating Champions Rulebook
Players take turns placing cards face-down and announcing their rank (e.g., "Two Aces"). The catch is that you don't actually have to play what you say. The Cheat: If someone suspects a lie, they yell "Cheat!". If correct: The cheater picks up the entire discard pile. If wrong: The accuser picks up the pile. family cheaters game link
Hasbro released an official version of Monopoly that turns "house rule" cheating into actual mechanics. Several newer family games are built entirely around