The Development of Complex Oligopoly Dynamics Theory

This chapter will review the development of the theory of complex oligopoly dynamics from the 1970s to the year 2001 in its main strands. It will also provide certain speculations regarding possible future developments. This will serve as a link between the first chapter’s discussion of the broader history of oligoply theory up to the 1940s and the more specific chapters that present current models in the rest of this book. But, to tell our story we first need to remind ourselves of certain ideas from the first chapter of this book. One is the very founding document of oligopoly theory, Cournot’s seminal work of 1838. This is both because the specific model that he presented has been much studied for its ability to generate complex dynamics and also because of its more general foreshadowing of game theory. It has often been noted that the Cournot equilibrium is but a special case of the Nash (1951) equilibrium, the more general formulation used by modern industrial organization economists in studying oligopoly theory. Indeed, it is sometimes even called the Cournot-Nash equilibrium. Although many of the models of complex oligopoly dynamics use the specific Cournot model, many use more general game theoretic formulations. We note simply as an aside here that Cournot’s work was the first to apply calculus to solving an economic optimization problem and also was the first to introduce supply and demand curves, albeit in the “Walrasian” form with price on the horizontal axis.