Game theory analysis is a useful tool to study the behaviour of firms in oligopolistic markets- the fundamental economic problem of competition between two or more firms. In this essay I will focus on two of the most notorious models in oligopoly theory; Cournot and Bertrand. In the Cournot model, firms control their level of production, which influences the market price. In the Bertrand model, firms decide on what price to set for a unit of product, which affects the market demand. Competition in oligopoly markets is a setting of strategic interaction which is why it is analyzed in a game theoretic context.

Both Cournot and Bertrand competition are modelled as strategic games. In addition, in both models a firm’s revenue is the product of a firms part of the market multiplied by the price. Furthermore, a firm incurs a production cost, which is dependant on its production level. In the simplest model of oligopolistic competition firms play a single game, where actions are taken simultaneously. All firms produce homogenous goods and demand for this good is linear and the cost of production is fixed per unit. In this market a Nash equilibrium in pure strategies exists in both the Cournot and Bertrand models. However, despite the many parallels between the models, the Nash equilibrium points are extremely different. In Bertrand competition, Nash equilibrium drives prices down to the same level they would be under perfect competition (p=MC), while in Cournot competition, the price at Nash equilibrium is unquestionably above the competitive level.

Cournot and Bertrand Competition

In 1838 Augustin Cournot published ‘Recherches sur les Principes Mathematiques de la Theorie des Richesses’, a paper that laid out his theories on competition, monopoly, and oligopoly. However Joseph Louis François Bertrand concluded that Cournots equilibrium for duopoly firms was not accurate. He went on to argue ‘whatever the common price adopted, if one of the owners, alone, reduces his price, he will, ignoring any minor exceptions, attract all of the buyers, and thus double his revenue if his rival lets him do so’.

Cournot had originally arrived at his