Synchronization and Global Dynamics of a Cournot Model with Nonlinear Demand and R&D Spillovers

In this paper, a dynamical Cournot model with nonlinear demand and R&D spillovers is established. The system is symmetric when the duopoly firms have same economic environments, and it is proved that both the diagonal and the coordinate axes are the one-dimensional invariant manifolds of system. The results show that Milnor attractor of system can be found through calculating the transverse Lyapunov exponents. The synchronization phenomenon is verified through basins of attraction. The effects of adjusting speed and R&D spillovers on the dynamical behaviors of the system are discussed. The topological structures of basins of attraction are analyzed through critical curves, and the evolution process of “holes” in the feasible region is numerically simulated. In addition, various global bifurcation behaviors, such as two kinds of contact bifurcation and the blowout bifurcation, are shown.

Green Innovation and Competition: R&D Incentives in a Circular Economy

The present paper provides theoretical insights regarding the determinants of firms’ incentives to invest in a Circular Economy. The analysis relies on a Cournot model disaggregating the disposal cost in the production function. In a non-simultaneous sequential game, two risk-neutral firms are endowed with a green innovation project that, if successful, would reduce the overall production costs and implement a Circular Economy. Firms are plagued by asymmetric information about the exact value of the other firm’s innovation. In this setting, the R&D investment in a Circular Economy, by affecting the distribution of production and disposal costs, influences the production decisions of both the innovating and the rival firms. The sign of the impact depends on the firms’ strategy in the product market. Furthermore, the analysis points out that cooperation in R&D of firms competing in the product market reinforces incentives to invest in green innovation. This suggests that governments aimed to advance a Circular Economy should encourage firms’ cooperation.

A Full Description of ω-Limit Sets of Cournot Maps Having Non-Empty Interior and Some Economic Applications

Given a continuous Cournot map F(x,y)=(f2(y),f1(x)) defined from I2=[0,1]×[0,1] into itself, we give a full description of its ω-limit sets with non-empty interior. Additionally, we present some partial results for the empty interior case. The distribution of the ω-limits with non-empty interior gives information about the dynamics and the possible outputs of each firm in a Cournot model. We present some economic models to illustrate, with examples, the type of ω-limits that appear.

Analysis on the Production and Marketing Strategies of Oligopoly Companies Based on Cournot Model and Stackelberg Model

By comparing Cournot model and Stackelberg model under complete information market and Cournot model under incomplete information market, this paper analyzes the impact that manufacturer choose simultaneous or sequential games when determining the amount of output as well as the production and marketing strategy to maximize the profit of the manufacturers in the oligopoly market. A specific analysis is also conducted according to Gree air-conditioning manufacturer’s data.

Market Power in Output and Emissions Trading

This article focuses on the strategic behavior of firms in the output and the emissions markets in the presence of market power. We consider the existence of a dominant firm in the permit market and different structures in the output market, including Cournot and two versions of the Stackelberg model, depending on whether the permit dominant firm is a leader or a follower in the output market. In all three models, the firm that dominates the permit market is more sensitive to its initial allocation than its competitor in terms of abatement and less sensitive in terms of output. In all three models, output is decreasing and the permit price is increasing in the permit dominant firm’s initial allocation. In the Cournot model, permit dominance is fruitless in terms of output and profit if the initial allocation is symmetric. Output leadership is more relevant than permit dominance since an output leader always tends to, ceteris paribus, produce more and make more profit whether it also dominates the permit market or not. This leadership can only be overcompensated for by distributing a larger share of permits to the output follower, and only if the total number of permits is large enough. In terms of welfare, Stackelberg is always superior to Cournot. If the initial permit allocation is symmetric, welfare is higher when the same firm dominates the output and the permit market at the same time.