Under certain conditions, a government can run a "rational Ponzi game," i.e., issue debt and never repay any interest or principal. Does Ricardian equivalence hold with respect to a tax cut that is financed by such a scheme? We study this question using overlapping generations models in which generations are linked by gifts or bequests. We find that although there are multiple equilibria, Ricardian equivalence can hold, and often seems to be the most natural outcome.