Bertrand Competition - Critical Analysis of The Bertrand Model

Critical Analysis of The Bertrand Model

The Bertrand model rests on some very extreme assumptions. For example, it assumes that consumers want to buy from the lowest priced firm. There are various reasons why this may not hold in many markets: non-price competition and product differentiation, transport and search costs. For example, would someone travel twice as far to save 1% on the price of their vegetables? The Bertrand model can be extended to include product or location differentiation but then the main result - that price is driven down to marginal cost - no longer holds. With search costs, there may be other equilibria apart from the competitive price - the monopoly price or even price dispersion may be equilibria as in the classic "Bargains and Rip-offs" model.

The model also ignores capacity constraints. If a single firm does not have the capacity to supply the whole market then the "price equals marginal cost" result may not hold. The analysis of this case was started by Francis Ysidro Edgeworth and has become known as the Bertrand-Edgeworth model. With capacity constraints, there may not exist any pure strategy Nash equilibrium, the so-called Edgeworth paradox. However, in general there will exist a mixed-strategy Nash equilibrium as shown by Huw Dixon

There is a big incentive to cooperate in the Bertrand model: colluding to charge the monopoly price and sharing the market each is the best that the firms could do in this set up. However not colluding and charging marginal cost, is the non-cooperative outcome and the only Nash equilibrium of this model. If we move from a one-shot game to a repeated game, then perhaps collusion can persist for some time or emerge.