The aim of the present paper is to attack some of the conceptual problems that arise when the framework of mathematical learning theory is applied to the description of the behavior of the finn, in setting prices and production quotas, in a competitive market. The goal is to depict the process by which the firm fixes prices and production quotas as a stochastic learning process. A solution to such problems is proposed which is based on statistical-decision concepts. The conceptualization of the behavior of the firm by means of concepts pertaining to mathematical learning theory gives rise to certain mathematical problems, which are formulated here in rather precise terms.
It is usual to find in competitive markets that one and the same type of good (perhaps with some slight variations in quality, presentation and so on) is produced by different firms. A typical example nowadays is the proliferation in the markets of North America of the so-called PC-compatible personal computers. There are certain lines among these machines which are so similar, that for all practical purposes they can be considered as equal. When a number of firms are producing the same type of good under competitive conditions, the process of price formation has certain peculiarities which are not present under monopolistic conditions. The aim of price formation dynamics (PFD) is precisely to provide a theory of the process of price formation under competitive conditions (although oligopoly is one particular, limit case) for firms producing the same type of good. The usual story is that each firm has a closed and convex production set Y representing its limited technological knowledge, that it faces a price system P=(Pl ..... p,) (where n is the number of goods in the economy), and that its behavior consists in choosing a point x* in Y that maximizes its profits given the price p, subject to restrictions in initial capital availability and credit. The real story, however, might be different and less deterministic. The contention of PFD is that it is the firm of the agent that in fact fixes both the price and the production quota for its goods and, moreover, that the process of fixing these magnitudes is one of trial and error. More precisely, the claim of PFD is that the process by which the firm fixes prices and production quotas Erkenntnis 30 (1989) 87-99.