Beckmann's Bertrand–Edgeworth duopoly model: new pure strategy equilibria

In this paper, the concept of weak active equilibrium, which was introduced in the eighties of the twentieth century by Smol'yakov, is used for the first time for a study of Bertrand–Edgeworth oligopoly (that is, competition among firms when firms' strategies are prices and firms' production capacities are limited). All symmetric weak active equilibria are found for the basic model of Bertrand–Edgeworth duopoly, which was analysed in the sixties of the twentieth century by Beckmann. However, this model is highly simplified. Also, the question of existence of nonsymmetric weak active equilibria is studied.