We study price competition in the presence of search costs and product differentiation. The limit cases of the model are the ‘‘Bertrand Paradox,’’ the ‘‘Diamond Paradox,’’ and Chamberlinian monopolistic competition. Market prices rise with search costs and decrease with the number of firms. Prices may initially fall with the degree of product differentiation because more diversity leads to more...

In 1903 Russell’s paradox came over the mathematical world with a double stroke. Bertrand Russell himself published it under the heading “The Contradiction” in chapter 10 of his Principles of Mathematics (Russell 1903 ). Almost at the same time Gottlob Frege (1848–1925) referred to Russell’s paradox in the postscript of the second and final volume of his Grundgesetze der Arithmetik (Frege 1903 ...

The Bertrand paradox holds that price competition among at least two firms eliminates all profits in equilibrium, when firms have identical constant marginal costs. This assumes that the number of competitors is common knowledge among firms. If firms are uncertain about the number of their competitors, there is no pure strategy equilibrium. But in mixed strategies an equilibrium exists. In this...

This paper analyzes a simple, repeated game of simultaneous entry and pricing. We report a surprising property of the symmetric equilibrium solution: If the number of potential competitors is increased above two, the market breaks down with higher probability, and the competitive outcome becomes less likely. More potential competition lowers welfare | another Bertrand paradox. The model can als...

We analyze the classical Bertrand model when consumers exhibit some strategic behavior in deciding from which seller they will buy. We use two related but different tools. Both consider a probabilistic learning (or evolutionary) mechanism, and in the two of them consumers’ behavior influences the competition between the sellers. The results obtained show that, in general, developing some sort o...

In [14] Matsuda and Yorozu.explained that there is no special Bertrand curves in Eⁿ and they new kind of Bertrand curves called (1,3)-type Bertrand curves Euclidean space. In this paper , by using the similar methods given by Matsuda and Yorozu [14], we obtain that bitorsion of the quaternionic curve is not equal to zero in semi-Euclidean space E4^2. Obtain (N,B2) type quaternionic Bertrand cur...

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...

Abstract In a recent article, P. Roger Turner and Justin Capes argue that no one is, or ever was, even partly morally responsible for certain world-indexed truths. Here we present our reasons thinking their argument is unsound: It depends on the premise possible worlds are maximally consistent states of affairs, which under plausible assumptions concerning demonstrably false. Our to show this b...