The identical agent, identical good Bertrand game is associated with prices at marginal cost the Bertrand Paradox. If consumers make occasional mistakes I show that the standard Bertrand game gives rise to positive profits and prices above marginal cost. Some firms charge low prices to capture the bulk of the sales while others charge high prices selling to mistaken consumers. Furthermore, with...

This paper provides a simple model of endogenous horizontal product differentiation that has two important implications. First, the model can explain the “empirical Bertrand paradox” – the failure to observe homogeneous product Bertrand oligopoly. If product differentiation is possible at reasonable cost, then Bertrand firms would always invest in product differentiation. Using a quadratic util...

The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geomet...

We show that bounded monopoly profits are essential for the uniqueness of the Bertrand paradox (zero profit) outcome. Otherwise, a folk theorem obtains for one-shot homogeneous product Bertrand games: any positive (but finite) payoff vector can be achieved in a symmetric mixed-strategy Nash equilibrium. JEL Numbers: D43, C72

We show that in a homogeneous-good duopoly market with quality uncertainty and constant unit costs, the Bertrand paradox (i.e., marginal cost pricing) can be avoided.

We show that there is a unique correlated equilibrium, identical to the unique Nash equilibrium, in the classic Bertrand oligopoly model with homogenous goods and identical marginal costs. This provides a theoretical underpinning for the socalled “Bertrand paradox” as well as its most general formulation to date. Our proof generalizes to asymmetric marginal costs and arbitrarily many players in...

Cournot and Bertrand oligopolies constitute the two most prevalent models of firm competition. The analysis of Nash equilibria in each model reveals a unique prediction about the stable state of the system. Quite alarmingly, despite the similarities of the two models, their projections expose a stark dichotomy. Under the Cournot model, where firms compete by strategically managing their output ...

The classical price competition model (named after Bertrand), prescribes that in equilibrium prices are equal to marginal costs. Moreover, prices do not depend on the number of competitors. Since this outcome is not in line with real-life observations, it is known as the “Bertrand Paradox”. Many theoretical problems with the original model have been considered as an explanation of the paradox i...