A model of a pure exchange economy is investigated without the usual assumption of convex preference sets for the participating traders. The concept of core, taken from the theory of games, is applied to show that if there are sufficiently many participants, the economy as a whole will possess a solution that is sociologically stable--i.e., that cannot profitably be upset by any coalition of traders.

This brief note is presented as a convenience for those who wish to see what an actual numerical example of a smooth trading economy with multiple equilibria looks like in terms of an Edgeworth box diagram. The authors present a two trader two commodity example in terms of a fanciful exchange between two kinds of money.

The purpose of this paper was to take a simple model of two firms in competition, with explicit cost functions and an explicit demand function, and to examine the behavior of the firms on the basis of each of several theories. It was assumed there is no collusion among the buyers, so that the demand function remains fixed and describes the action of the market. Each theory discussed, except the 'contract curve' of Edgeworth, gives a uniquely determined pair of production rates, and all the others, with the exception of the Von Neumann and Morgenstern solution, determine the profit made by each of the two producers. Graphs are given showing the production rates and profits for the various solutions, and will serve to compare the effect of the different formulations on the behavior of the firms.