On balancedness of superadditive games and price equilibria in exchange economies

Exchange economies with indivisible objects, money and quasi-linear utilities generate non-negative superadditive transferable utility (TU) games. If such an economy has a price equilibrium, then this TU game is balanced. In this note, we prove that the converse of this statement is also true, i.e. every non-negative superadditive and balanced TU game generates an exchange economy with a price equilibrium.