Core versus equilibrium allocations in economies with differential information

A neoclassical exchange economy consists of finitely many agents where each agent has a strictly monotone and strictly convex preference, and a non-zero initial endowment such that the total endowment is strictly positive. Applying analytic topological methods, Arrow and Debreu [1] proved the existence of a competitive equilibrium in such an economy. Furthermore, Scarf [10] proved that the core of a neoclassical exchange economy is non-empty and compact. It is not difficult to observe that every competitive equilibrium is a core allocation, but the converse does not hold in general. In 1964, Aumann [2] established an interesting result showing that the converse holds for an exchange economy with a continuum of agents. In 1979, Radner [9] introduced the concept of rational expectations equilibrium in economies in which traders have different information about the items to be traded. Since then, many mathematicians and economists have been trying to extend the aforementioned work of Nobel laureates Arrow, Debreu and Aumann to economies with differential information. Very often, studying such economies needs advanced techniques from modern analysis and topology. In this talk, I will present the recent research work of mine and my coauthors in this direction.