This paper considers an international financial problem of a sovereign country called debt overhang. The term "debt overhang" expresses the situation where a sovereign country has borrowed money from foreign banks and has been unable to fulfill the scheduled repayments for some period. We formulate this problem as a noncooperative game with n lender banks as players where each decides either to sell its loan exposure to the debtor country at the present price of debt on the secondary market, or to wait and keep its exposure. There are many pure and mixed strategy Nash equilibria in this game. However we show that in any Nash equilibrium, the resulting secondary market price remains almost the same as the present price when the number of banks is large. We also obtain the comparative statics result that in a mixed strategy equilibrium, banks with smaller loan exposures have a greater tendency to sell than banks with larger loan exposure. In addition, we discuss the structure of the set of Nash equilibria.