5 - Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives

Summary

In a game of a finite number of repetitions of a Cournot-type model of an industry, if firms are satisfied to get close to (but not necessarily achieve) their optimal responses to other firms' sequential strategies, then in the resulting noncooperative “equilibria” of the sequential market game, (1) if the lifetime of the industry is large compared to the number of firms, there are equilibria corresponding to any given duration of the cartel, whereas (2) if the number of firms is large compared to the industry's lifetime, all equilibria will be close (in some sense) to the competitive equilibrium.

Introduction

In 1838 Augustin Cournot introduced his model of market equilibrium, which has become known in modern game theory as a noncooperative (or Nash) equilibrium [1]. Cournot's model was intended to describe an industry with a fixed number of firms with convex cost functions, producing a homogeneous product, in which each firm's action was to choose an output (or rate of output), and in which the market price was determined by the total industry output and the market demand function. A Cournot-Nash equilibrium is a combination of outputs, one for each firm, such that no firm can increase its profit by changing its output alone.

Cournot thought of his model as describing “competition” among firms; this corresponds to what we call today the “noncooperative” character of the equilibrium.