Core versus equilibrium allocations in economies with differential information

A neoclassical exchange economy consists of ?nitely many agents where each agent has a strictly monotone and strictlyconvex preference, and a non-zero initial endowment such that the total endowment is strictly positive. Applying analytic topologi-cal 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 di?cult to observe that every com-petitive equilibrium is a core allocation, but the converse does not hold in general. In 1964, Aumann [2] established an interestingresult 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 di?erentinformation about the items to be traded. Since then, many mathematicians and economists have been trying to extend the afore-mentioned work of Nobel laureates Arrow, Debreu and Aumann to economies with di?erential information. Very often, studyingsuch economies needs advanced techniques from modern analysis and topology. In this talk, I will present the recent research workof mine and my coauthors in this direction.