Generalized equilibria in an economy without the survival assumption

It is well known that an equilibrium in the Arrow-Debreu model may fail to exist if a very restrictive condition called the survival assumption is not satisfied. We study two approaches that allow for the relaxation of this condition. Danilov and Sotskov (1990), and Florig (2001) developed a concept of a generalized equilibrium based on a notion of hierarchic prices. Marakulin (1990) proposed a concept of an equilibrium with non-standard prices. In this paper, we establish the equivalence between non-standard and hierarchic equilibria. Furthermore, we show that for any specified system of dividends the set of such equilibria is generically finite. We also provide a generic characterization of hierarchic equilibria and give an easy proof of the core equivalence result.