The well-known problem of classical mechanics considered by Bertrand (1857) and Darboux (1901) is reviewed in the context of Cartan’s geometry. UDK: 514.85; MSC: 37J35, 53C05

We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership — at least temporarily. We show that leapfrogging occurs in equilibrium, resolving the Bertrand investment paradox., i.e. leapfrogging explains why firms have an ex a...

This paper provides necessary and sufficient conditions for the existence of a pure strategy Bertrand equilibrium in a model of price competition with fixed costs. It unveils an interesting and unexplored relationship between Bertrand competition and natural monopoly. That relationship points out that the non-subadditivity of the cost function at the output level corresponding to the oligopoly ...

The Incentives for Takeover in Oligopoly* by Roman Inderst and Christian Wey This paper presents a model of takeover incentives in an oligopolistic industry, which, in contrast to previous approaches, takes both insiders' and outsiders' gains from an increase in industry concentration into account. Our main application is to compare takeover incentives in a differentiated Cournot and Bertrand o...