Welfare Economy under Rough Sets Information

This paper relates welfare economy and rough sets as information structure. We reconsider the fundamental welfare theorem for a pure exchange economy under uncertainty from the logical point of view in data mining theory; the traders are assumed to have a multi-modal logic of belief and to make their decision under uncertainty represented by rough sets. We propose a generalized notion of rational expectations equilibrium, called expectation equilibrium in belief for the economy, and we show an extension of the fundamental theorem for welfare: An allocation in the economy is ex-ante Pareto optimal if and only if it is an expectations equilibrium allocation in belief for some initial endowment with respect to some price system.