Linkedness of Allocations and the Rate of Convergence of the Core

Abstract

This paper is based on a theorem of Robert Anderson (1987) which proves that in a general sequence of finite economies with smooth preferences, the rate of convergence of the competitive gap with respect to the gap-minimizing prices is the inverse of the square of the number of agents. We argue that the assumptions of the theorem are too restrictive and try to relax some of them. We actually prove that the same rate of convergence can be obtained with a much weaker assumption called the uniform linkedness of allocations.