An Example of a Slow-Converging Core

This report concerns the shrinking of the core of a trading economy as the number of traders is increased without limit. While experience with replicated market models (i.e., increasing sequences of economies in which each trader type appears in a fixed proportion) suggests that the "normal" asymptotic rate of convergence of the core is inversely proportional to the number of traders, the present finding is that neither this nor any other rate can be guaranteed. This result seems to indicate that even in a "large" economic system, with many perfectly substitutable traders of every type, it is still possible for significant departures from pure competition to occur if the kind of collusion embodied in the core concept is not enjoined.