Imperfect Competition with Unknown Demand

The increased attention that has recently been directed at informational aspects of economic models clearly points to the need for a serious re-examination of certain traditional theories. Among those that suggest themselves for such a re-evaluation, theories in the general area of imperfect competition deserve a high priority, primarily because of the fact that firms operating in such markets are normally assumed to have complete knowledge of their demand functions. At the heart of this entire issue is one basic problem which may be stated quite simply by posing the following question: can one construct a meaningful and non-empty theory of imperfect competition without the assumption that firms have complete knowledge of their demand functions ? It is the purpose of this paper to show that the answer to this question is in the affirmative. We do this by constructing a model of an imperfectly competitive market in which each firm is assumed to have no information about its demand function (except that it is downward sloping), and we show that this model yields several testable hypotheses that are both interesting and reasonable. We should point out that the basic ideas and methods behind our approach are not entirely novel; efforts in similar directions may be found in the works of Arrow [1], Clower [2], and Day [3].