This paper retakes previous work of the authors, about the relationship between non-quasi-competitiveness (the increase in price caused by an increase in the number of oligopolists) and stability of the equilibrium in the classical Cournot oligopoly model. Though it has been widely accepted in...

This paper presents a classical Cournot oligopoly model with some peculiar features: it is non-quasi-competitive as price under N-poly is greater than monopoly price; Cournot equilibrium exists and is unique with each new entry; the successive equilibria after new entries are stable under the...

The approximants to regular continued fractions constitute "best approximations" to the numbers they converge to in two ways known as of the first and the second kind. This property of continued fractions provides a solution to Gosper's problem of the batting average: if the batting average of a...

We start with a generalization of the well-known three-door problem: the n-door problem. The solution of this new problem leads us to a beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions...

Theorem 1 of Euler's paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum one. Euler attributes the Theorem to Goldbach. The proof is one of those...