On Dynamic Investigations of Cournot Duopoly Game: When Firms Want to Maximize Their Relative Profits

This paper studies a Cournot duopoly game in which firms produce homogeneous goods and adopt a bounded rationality rule for updating productions. The firms are characterized by an isoelastic demand that is derived from a simple quadratic utility function with linear total costs. The two competing firms in this game seek the optimal quantities of their production by maximizing their relative profits. The model describing the game’s evolution is a two-dimensional nonlinear discrete map and has only one equilibrium point, which is a Nash point. The stability of this point is discussed and it is found that it loses its stability by two different ways, through flip and Neimark–Sacker bifurcations. Because of the asymmetric structure of the map due to different parameters, we show by means of global analysis and numerical simulation that the nonlinear, noninvertible map describing the game’s evolution can give rise to many important coexisting stable attractors (multistability). Analytically, some investigations are performed and prove the existence of areas known in literature with lobes.

Environmental Management through Coopetitive Urban Waste Recycling in Eco-Industrial Parks

In this article, we consider the coexistence of competing actors within a specific eco-industrial park. The competing firms dynamics evolves by means of an interplay agreement determined among the competitors themselves. In particular, we show a possible scenario in which the selected eco-industrial competitors could greatly benefit from a coopetitive interaction, within their common eco-park, while improving the general conditions of a near residential area. The associated dynamical coopetitive agreement, aims at the growth and improvement of the firms themselves and of their industrial network (within a virtuous environmental path). As an example, we assume the existence of two competitors selling the same good on the same market, so that, from a competitive point of view, we construct a classic Cournot duopoly model upon which we build up a multidimensional coopetitive agreement. Our eco-friendly deal allows to “enlarge the pie” of possible gains by diminishing sunk costs and other forms of costs, especially the environmental costs associated to the management of urban waste recycling. Consequently, we suggest production methods and production quantitative profiles in order to “share the gains fairly”. We show a complete mathematical analysis of our new economic game and show some of its possible and relevant solutions.

Differentiated Entry or “Me-Too” Entry in Bertrand and Cournot Oligopoly

When would an oligopolistic entrant imitate an incumbent’s product (“me-too” entry), rather than horizontally differentiate? We allow an entrant's product choice to vary endogenously with the cost of product differentiation. Such endogenity of product differentiation significantly affects the comparison of Bertrand and Cournot duopoly. We find that if Bertrand entry occurs, products are differentiated, whereas there is a substantial region in which Cournot entry involves a homogenous product. Bertrand prices may be higher than Cournot prices; and, if product differentiation costs are low enough to induce Cournot differentiated entry, then Bertrand industry profit equals or exceeds Cournot industry profit.

DOMINANT STRATEGIC TRADE POLICY

In implementing trade policy measures, governments usually select from a range of instruments including quotas, subsidies (explicit or implicit) and tariffs. In this paper we consider the potential gain of a government pursuing a two-part trade policy: an import license for entry, along with a per-unit tariff on imports. The model is a three-step game between home and foreign countries in the Cournot duopoly. The paper demonstrates that two-part trade policy is dominant.

Strategic trade policy with interlocking cross-ownership

By analysing interlocking cross-ownership, this work reconsiders the inefficiency of activist governments that set subsidies for their exporters (Brander and Spencer, J Int Econ 18:83–100). Making use of a third-market Cournot duopoly model, we show that the implementation of strategic trade policy in the form of a tax (subsidy) when goods are differentiated (complements) is Pareto-superior to free trade within precise ranges of firms’ cross-ownership, richly depending on the degree of product competition. These results challenge the conventional ones in which public intervention (1) is always the provision of a subsidy and (2) always leads to a Pareto-inferior (resp. Pareto-superior) equilibrium when products are substitutes (resp. complements).