What are feasible paths of debt for a government that borrows either internally or externally? The question is suggested by recent concerns about the international debt crisis and high federal budget deficits in the U.S. In this paper, we analyze the benchmark case in which all market participants have perfect foresight, so that only risk-free lending is done. We study the conditions under which the borrower's opportunities include strategies with positive net present value. The strategies we investigate are perfect foresight versions of the "Ponzi schemes" discussed by Minsky (1982) and Kindleberger (1978), where individuals or companies pay out funds to some parties by borrowing funds from others. Since the perfect foresight assumption rules out schemes based on imperfect information (e.g., swindles) or irrationality of lenders (e.g., fallacies of composition), we are asking under what circumstances these Ponzi games can continue indefinitely. When, in other words, is it feasible for a government to incur debt and never pay back any principal or interest? We call such a policy, where all principal repayments and interest are forever "rolled over," i.e., financed by issuing new debt, a "rational Ponzi game.