A game between the IMF, a country, and atomistic private investors is motivated by recent crises including Argentina. The one stage game has no Nash equilibrium in pure strategies. Considering an equilibrium in mixed strategies, conditions are derived on whether the IMF should exist. A "cooperative first best" may be supported in a repeated game by a "minimum punishment strategy" but breaks down as the probability of insolvency rises. Countries are likely to deviate in bad times placing the IMF in an "impossible position. The international financial architecture (IFA) remains incomplete.