Competitive equilibrium with indivisible goods and symmetry

Abstract This study analyzes exchange economies in which all players have the same utility function and all goods except money are indivisible. In this context, a necessary and sufficient condition for the existence of a competitive equilibrium is obtained based on the fact that certain associated cooperative games have a non-empty core. Based on this result, we find two conditions in the cardinal case, each of which is equivalent to the existence of an equilibrium in an economy. By introducing the $$\alpha $$ -concavity property, we obtain another sufficient (although not necessary) condition for the existence of an equilibrium. The study also proposes an algorithm to determine whether a cardinal economy has an equilibrium and, if so, to obtain the equilibrium price.