Knowledge that Transforms

Harsanyi [1], after translating Zeuthen's bargaining theory [5, Ch. 4] into modern utility terms, has shown that it implies the same outcome as Nash's theory [4], namely a settlement that maximizes the product of the utility increments of the two parties. In the same paper, Harsanyi also reviewed Hicks's comparable theory [2, pp. 140-45] and found it, understandably, distinctly inferior to Zeuthen's. The context that both Zeuthen and Hicks had in mind was labor-management bargaining, where agreements and conflicts have time dimensions. Specifically in such situations, it will be suggested, it is possible to combine the central conceptions of both Zeuthen and Hicks in a composite theory that is superior to either of the separate ones. To prepare the way for the composite theory's presentation, its components will be briefly summarized.

It is suggested that the most natural mathematical model for a market with perfect competition is one in which there is a continuum of traders (like the continuum of points on a line). It is shown that the core of such a market coincides with the set of its allocations, i.e., allocations which constitute a competitive equilibrium when combined with an appropriate price structure.