Information, Theories of Competition, and the Theory of Games

ECONOMIC theorists have dealt with monopolistic and oligopolistic competition, on the one hand, and pure competition, on the other; yet little effort has been made to unify these various theories of competition. This short note suggests a method of unifying these theories by means of game and information theory. Oligopoly theory has been treated in two ways. One is essentially static and assumes complete information to be present, as in the theory of games.2 The other assumes lack of complete information. The latter treatment has led to ideas of conjectural interdependence. The mathematical models of Cournot and Bertrand are of this variety. When dealing with the problem formulated in this manner, it is difficult to distinguish between statics and dynamics. The literature is not clear, even in the Cournot duopoly case, as to whether or not each production adjustment is meant to represent one period. Is it to be regarded as taking place instantaneously or possibly only taking place in the entrepreneurs' minds until they both produce at the equilibrium rate?3 In pure competition theory, the problem of information is dealt with by saying that each competitor knows that he cannot influence the market; hence he engages in a simple maximization problem. Professor Viner has suggested that pure competition does not imply complete information but implies equal ignorance on the part of all competitors. Professor Knight suggests: "Chief among the simplifications of reality prerequisite to the achievement of perfect competition is, as has been emphasized all along, the assumption of practical omniscience on the part of every member of the competitive system."4 Professor Morgenstern has pointed out the error in Knight's statements yet very little formal analysis of the information aspects of pure competition has been done. The theory of monopoly deals with one individual maximizing against either an inanimate object in the market case or with a machine with a given law of motion in the long-run equilibrium case. For the market situation, the monopolist is assumed to know some sort of demand curve or function between price and quantity taken. In the long-run situation, sociological, psychological, or economic reasons can be thrown in; and the monopolist's reaction to a shift in the demand curves caused by any one of these reasons can be studied. A degree of uncertainty can be introduced by setting up the problem in a manner amenable to period analysis and then giving the monopolist only a probability distribution over the possible shapes of the future-demand curves I This research was partially supported by the Office of Naval Research, Contract N6onr-27009.