In this paper, we derive a cost-minimizing approach for governments in the eurozone that have to define their debt structure in terms of currency of issuance and maturity. We introduce and characterize the concept of weighted coalitional αα-equilibrium to assure stability of two tiers of the eurozone, the stronger (White) countries and the weaker (Yolk) countries. The equilibrium presents both the Pareto optimality of the countries in each tier and the stability against any deviation of each subcoalition. In a practical way, it would require either strong political integration within each tier or considerable market pressure.