Discrete representations of a continuum economy (Q1397605)

In this paper an atomless economy is considered in which the continuum of agents is represented by a real interval. By dividing the interval and associating to every agent in each subinterval the same initial endowments and preferences, there are defined sequences of discrete economies as approximations to the initial continuum economy. There are obtained convergence results for the core of the continuum economy in terms of the cores of the approximating discrete economies. Some counterexamples which provide a boundary for more general results are stated.