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History of Political Economy 35.2 (2003) 175-204
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The Conjectural Variations Approach to Duopoly Theory
It is a well-recognized peculiarity of the so-called years of “high theory” that for the first time in the history of economics the mental variables—that is, the expectations, conjectures, and beliefs—of the agents featuring in economic models gained the spotlight and became the explicit object of formal analysis. This happened as a consequence of the effort to extend the notion of static equilibrium to a multiperiod setup. Thus, elements such as an agent's knowledge, uncertainty, and foresight became absolutely central, so much so that, following G. L. S. Shackle's 1967 classic, it became commonplace to single them out as the leading topics during the period ranging from the mid-1920s to the early 1940s. Indeed, it was deemed impossible even to define the notion of economic equilibrium without relating it to the time dimension and to planning behavior, that is, without specifying how an agent's mental variables are formed and how economic interactions are framed in a multiperiod horizon. Crucial notions in contemporary economics such as temporary and intertemporal equilibrium or the ex ante–ex post distinction bear witness to the achievements of the “high theorists.”
In a single paper one cannot even briefly sketch the main events and characters leading to the rise of mental variables in interwar economics. Luckily, we already have some brilliant accounts of these developments [End Page 175] as they took place in the key fields of general equilibrium and business cycle theory.1 However, there does not exist an equivalent amount of work covering the similar developments that occurred in the same period in another crucial field, that of imperfect competition theory. We have indeed a rich literature dedicated to, say, the Sraffian critiques of Marshallian cost curves, the debate over Clapham's empty boxes, and Robinson's and Chamberlin's books, to name a few, but the focus is always upon either the mechanical or the empirical side of imperfect competition. This is rather peculiar, since the interaction between oligopolists offered the interwar economists the most natural ground for the first theoretical investigations of the formation and revision of the agents' expectations and multiperiod plans. While an exhaustive reconstruction of the development of oligopoly theory during the years of “high theory” would be a daunting task, in what follows I will tackle a rather limited topic, namely, the interwar debate over the determinateness of the solution for the standard Cournot duopoly model with quantity competition. As I show in this essay, the main outcome of the debate was the acknowledgment of the necessity to explicitly take into account each firm's conjectures in order to provide such a solution. Thus, 1920s–1930s duopoly theory should be recognized as another instance of the rise of mental variables—something that seems to have escaped existent narratives.
Starting from A. L. Bowley's 1924 Mathematical Groundwork and from the 1924 edition of A. C. Pigou's Economics of Welfare, the idea began to spread that the Cournot-style reaction functions of the duopolists had to be given a conjectural interpretation. The problem was that of reconciling the reaction functions—an allegedly dynamic concept—with the static setup of the Cournot model.2 The latter ambiguously mixed a static formalization of what today would be called a one-shot simultaneous game with a dynamic story in terms of each firm's actions, reactions, and counterreactions that would be better modeled as a sequential game. In particular, Cournot's reaction functions were formulated as a static equilibrium notion but had as argument the actual output produced by the other firm, a piece of information that each firm could possess only [End Page 176] in a sequential game. Yet, as is well known, the feature of the Cournot model that raised the most objections was another one, namely, the assumption that each firm behaved as if its rival would not react to its own move. This assumption was really puzzling, because...