Cobb-Douglas Preferences and Pollution in a Bilateral Oligopoly Market

In this paper, we investigate how pollution changes with preferences, focusing on a finite bilateral oligopoly model where agents have asymmetric Cobb-Douglas preferences. Producers are also consumers and the choice of heterogeneous preferences is related to the psychological foundations and identity aspects of group membership. We compare two strategic equilibria: the Stackelberg-Cournot equilibrium with pollution (SCEP) and the Cournot equilibrium with pollution (CEP). We show that considering the asymmetric preferences helps the public decision-maker to identify precisely the category of agents (consumer–producers or pure-consumers) for which a change in environmental preference parameters will most effectively reduce pollution. Furthermore, we find that firms’ emissions’ elasticity decreases with market power (when the market power increases) if their marginal cost is lower than their competitor. Finally, we show that when producers are also consumers, an action on pure-consumers’ preference parameters reduces more emissions than a similar action on consumer–producers, and this regardless of the timing of interaction.

A Stackelberg–Nash–Cournot Equilibrium in a Pollution Reduction Scheme

This paper presents a Stochastic Stackelberg–Nash–Cournot Equilibrium model with continuous market demand distribution to examine the effectiveness of ambient charges as an effective policy measure for reducing nonpoint source pollution in a hybrid scheme. To do so, we consider the supply side of an energy market with hybrid technology that competes in an oligopoly market setting. Within such a setting, each power plant or firm uses a mix of fossil fuels (F) and renewable energy sources (R) to generate power at any given time. The demand for electricity is not realized at the time when the firm (leader) makes the decision. The competition between the two energy sources available to leader is assumed to be of Nash–Cournot equilibria, implying that they use one energy source to generate electricity, whilst holding the other energy source as a constant when the followers reactions are known. Based on the assumption that the demand function is affine and power plants cost functions are quadratic, we obtain the Stackelberg–Nash–Cournot equilibrium. Hence, our analysis provides an interesting insight into the effectiveness of using ambient charges, within the context of a Stochastic Stackelberg–Nash–Cournot competition, as an environmental economic policy measure when included within a robust hybrid scheme. From an economical point of view, this allows pollutants to develop specific control technologies by undertaking research and development (R&D) measures or production processes to maintain emissions standards in a hybrid scheme. From a policy implementations point of view, the environmental authority can use the pollution abatement technology ratio to set ambient charges and industry specific pollutant quantitative limits subject to technological variations.

Two extensions of consumer surplus

We study consumer surplus in a single market when (a) there is a lower bound in the consumption of the outside good and (b) the weights in the social welfare function given to consumers and firms are different. We assume quasilinear utility. When the lower bound constraint on the consumption of the outside good is binding, income effects arise in demand. In some cases, Cournot equilibrium output is below equilibrium output without this constraint because the constraint makes demand less elastic. When the weights given to consumers and firms are not identical, social welfare is not necessarily concave and profits might be negative at the unrestricted optimum. We characterize social welfare optimum with a bound on maximum losses in a class of utility functions. We offer a formula to find the percentage of welfare losses due to oligopoly in this case.

An inertial iterative scheme for solving variational inclusion with application to Nash-Cournot equilibrium and image restoration problems

Variational inclusion is an important general problem consisting of many useful problems like variational inequality, minimization problem and nonlinear monotone equations. In this article, a new scheme for solving variational inclusion problem is proposed and the scheme uses inertial and relaxation techniques. Moreover, the scheme is self adaptive, that is, the stepsize does not depend on the factorial constants of the underlying operator, instead it can be computed using a simple updating rule. Weak convergence analysis of the iterates generated by the new scheme is presented under mild conditions. In addition, schemes for solving variational inequality problem and split feasibility problem are derived from the proposed scheme and applied in solving Nash-Cournot equilibrium problem and image restoration. Experiments to illustrate the implementation and potential applicability of the proposed schemes in comparison with some existing schemes in the literature are presented.

GAME EQUILIBRIUM BASED CONTROL ANALYSIS ON THE SUSTAINABLE MARKET STRUCTURE OF RARE METAL MINERAL RESOURCES – EVIDENCE FROM CHINA

In rare metal mineral market, as a complex system, multiple decision-making among the stakeholders increases the complexity in its market structure and dynamic process. The unreasonable compensation pricing mechanism for the development of the rare metal mineral resources in China requires to be studied. Drawing on the methods of game theory model and chaos control analysis, this paper builds theoretical model of rare metal mineral market structure, corporating related parameters of rare metal in the game theory model, to conduct the chaotic nature and path analysis, expecting to solve the bottleneck problems that restrict the rare metal pricing and resource security and enhance the waste valorization for the sustainability. Specificly, a Cournot-Nash Equilibrium model is built to analyze the Cournot-equilibrium point, the stability of the Cournot Equilibrium point, the chaotic status, as well as the pattern to chaos of the game system in the rare metal mineral resource market, numerical simulation is used to verify the model. The conclusions facilitate the formulation of industrial economic policies and further improvement of managerial strategies to solve market problems.

Local Stability of Cournot Equilibrium as the Number of Firms Increases

In this paper, a Cournot oligopoly with isoelastic demand function and constant marginal cost is considered. The local stability conditions of the Cournot equilibrium are determined for four models with different decision mechanisms. In the first model, firms adjust their outputs using the best reply response with naive expectations. The second model is a generalization of the first one, where firms have adaptive expectations. Meanwhile, the third and fourth models adopt the bounded rationality and local monopolistic approximation, respectively. The results show that, in the case of identical firms, the Cournot equilibrium is always stable when the firms adopt the local monopolistic approximation mechanism.

Efficiency of Cournot and Bertrand Equilibria with Non-cooperative and Cooperative R&D in Presence of Product Differentiation

Strategic cooperative and non-cooperative R&D decisions are analysed in the presence of R&D spillover and product differentiation. Using a two-stage game it is shown that in both Cournot and Bertrand duopolies, R&D and output levels are larger and prices are lower under cooperative R&D agreements compared to non-cooperative R&D. For complementary and independent goods, these results are valid for any degree of R&D spillover and may hold for substitute goods even for sufficiently small R&D spillover. In terms of social welfare, cooperative R&D agreements dominate non-cooperation for both Cournot and Bertrand duopolies. As for relative efficiency of Cournot and Bertrand equilibria, it is shown that the traditional efficiency ranking may be reversed and Cournot equilibrium may dominate Bertrand equilibrium if the degree of product differentiation is low and the products are reasonably close substitutes for high degree of R&D spillover provided that R&D productivity is high. This result is stronger for cooperative R&D decision. JEL Codes: D21, D43, L13