Is there a name for this joke format?
I think it descends from a line about labor in the USSR: "We pretend to work, and they pretend to pay us." Tony Judt in "Thinking the Twentieth Century" had a line about Moscow needing its satellite states to avoid loudly or conspicuously disagreeing with party ideology even if in practice they were able to diverge. "You pretend to believe and we'll pretend to believe you."