Reducing competitors in a Cournot–Theocharis oligopoly model

Abstract

We study how firms disappear from the market in a Cournot -Theocharis oligopoly model. We find necessary and sufficient conditions for the global convergence of the system to a monopoly or a duopoly. In particular, we prove that when the number of firms increases, it is more difficult to eliminate a firm from the market.

Theocharis Problem Reconsidered in Differentiated Oligopoly

“…Our next research project will be to analyze nonlinear oligopolies and investigate their local and global stability. Further the nonnegativity of the outputs of the firms as well as taking capacity limits into account can be done similarly to Cánovas [20] and Bischi et al [21]. The resulting model becomes nonlinear making asymptotic analysis a bit more complicated, which will be worked out in our future research.…”

“…Comparison of Bertrand and Cournot oligopolies is discussed in Okuguchi [16], Vives [17], and Cheng [18] among others. More recently, taking into account of the nonnegativity constraints on the variables, Cánovas et al [19] consider the global dynamics to show that the -firm model has simple dynamics (i.e., it converges either to a monopoly or a duopoly or to a two-periodic oscillation), whose results are further extended in Cánovas [20].…”

Monopoly conditions in a Cournot-Theocharis oligopoly model under adaptive expectations

“…This fact introduces a non-linearity in the model. Other aspects have also been considered in [1], where it is studied how firms disappear from the market characterizing the global convergence of the system to a monopoly or a duopoly. In addition, A. Matsumoto and F. Szidarovszky [9] have studied Theocharis-Cournot model as a differentiated oligopoly.…”

“…Observe that for λ = 0 the system is trivially constant. On the other hand, λ = 1 represents "naive expectations" (3), which has already been studied in [1,2,13]. For convenience in the notation we define the maps F i : R n → R for i = 1, .…”

“…We say that a oligopoly globally converges to a monopoly, or that evolves to a monopoly, if lim t→∞ q i (t) = 0 for i = 1, ..., n − 1. For naive expectations, the characterization of the convergence to monopoly of an initial oligopoly was given in [1] by the following theorem. 1.…”