Cournot Equilibrium Research Articles

A joint Cournot equilibrium model for the hydrogen and electricity markets

Hydrogen production through renewable energy-powered electrolysis is pivotal for fostering a sustainable future hydrogen market. In the electricity sector, hydrogen production bears an additional demand that affects electricity price, and mathematical models are needed for the joint simulation, analysis, and planning of electricity and hydrogen sectors. This study develops a Cournot and a perfect competition model to analyze the links of the electricity and hydrogen sectors. In contrast to other solving methods approaches, the Cournot model is solved by convex reformulation techniques, substantially easing the resolution. The case studies, focusing on the Iberian Peninsula, demonstrate the region's potential for competitive hydrogen production, and the advantages of perfect competition to maximize the use of renewable energies, in contrast to Cournot's oligopoly, where the exercise of market power raises electricity prices. Sensitivity analyses highlight the importance of strategic decision-making in mitigating market inefficiencies, with valuable insights for stakeholders and policymakers.

Nash–Cournot Equilibrium and Its Impact on Network Transmission Congestion

This paper evaluates the impact of congestion on transmission lines when the operation cost is minimized using economic dispatch (ED), comparing the results obtained with the Nash–Cournot Equilibrium (NCE). A methodology is developed for the optimal power flow solution through the NCE, considering the network topology (upper and lower generation limits, upper and lower limits of the transmission lines, and power balance) for a nine-node system without and considering two bilateral power transactions. The results show that the operation cost is higher when the NCE is implemented than ED. However, the problem of congestion in the transmission lines is reduced due to the equilibrium obtained in the power dispatch against minimizing the operation cost in the dispatch; the transmission lines with the most significant participation tend to become congested when additional bilateral transactions occur. Finally, the above is verified by obtaining the mean and median of the transmission line percentages used in the two simulations.

One region's gain is another's loss: The impact of market segmentation on renewable energy development in China

Current research has focused on the effects of policy and economic factors on renewable energy (RE) development but has ignored the effects of market segmentation. We developed a two-stage Cournot equilibrium model to explore the relationship between the market segmentation behaviors of local governments and their effects on RE development. We empirically tested the spatial effects of market segmentation by using a spatial Durbin model based on panel data of Chinese provinces from 2006 to 2020. The results are as follows. (1) There are positive spatial dependences among the RE development in the provinces. Most provinces show a “high-high” or “low-low” spatial agglomeration pattern. (2) Market segmentation caused by local protection can promote local RE development but significantly inhibits the development of RE in neighboring regions, i.e., one region's gain is another's loss. The inhibition is much greater than the local development, thus hindering overall RE development. (3) Regions with more stringent environmental regulations have greater incentives to adopt the market segmentation strategy in order to promote local RE development. (4) Market segmentation can increase the degree of local capital and labor mismatch, thereby promoting local RE development and hindering RE development in neighboring regions.

Imitation Dynamics in Oligopoly Games with Heterogeneous Players

We investigate the role and performance of imitative behavior in a class of quantity-setting, Cournot games. Within a framework of evolutionary competition between rational, myopic best-response and imitation heuristics with differential heuristics’ costs, we found that the equilibrium stability depends on the sign of the cost differential between the unstable heuristic (Cournot best-response) and the stable one (imitation) and on the intensity of the evolutionary pressure. When this cost differential is positive (i.e., imitation is relatively cheaper vis a vis Cournot), most firms use this heuristic and the Cournot equilibrium is stabilized for market sizes for which it was unstable under Cournot homogeneous learning. However, as the number of firms increases (n=7), instability eventually sets in. When the cost differential is negative (imitation is more expensive than Cournot), complicated quantity fluctuations, along with the co-existence of heuristics, arise already for the triopoly game.

Comparison of the Optimal Policies on International Product R&D under Price and Quantity Competition

Purpose - The first objective is to analyze and compare Bertrand and Cournot equilibria in a model wherein two governments compete with regard to research and development (R&D) subsidies, and two firms compete in a third-country market through product R&D investment and substitute goods. The second purpose is to compare the results derived in the presence of government intervention in international trade with those obtained in the case of no-trade and non-intervention.
 Design/Methodology/Approach - For this analysis, we extend Symeonidis’s (2003) work and develop an international R&D subsidy game consisting of three stages.
 Findings - First, the equilibrium levels of R&D expenditure, product quality, subsidies, prices, and firm profits are higher under quantity competition compared to price competition in the presence of government intervention in international trade, as in Symeonidis’s (2003) no-trade and non-intervention model. Second, the rankings of output and consumer surplus in the third country under the two competitions differ from those derived by Symeonidis (2003), who finds that they depend on the degree of horizontal differentiation and R&D spillovers. Third, the ranking of social welfare under the two regimes differs from the results of Symeonidis (2003), who establishes that the ranking of social welfare depends on the degree of horizontal differentiation and R&D spillovers.
 Research Implications - If a country is involved in international trade with substitute goods and its government faces R&D subsidy competition in the presence of product R&D spillovers, it is better for the government to provide R&D subsidies to domestic firms under quantity competition rather than those under price competition to ensure greater social welfare.

Comparison between Simultaneous and Sequential Movements in a Duopoly Game

In general, a Stackelberg competition benefits the leader and the consumer due to making the first move in a sequential game. However, in this paper, sequential movement does not offer an advantage over simultaneous movement in a static duopoly under quantity competition with an isoelastic demand function. By introducing dynamics into the duopoly model through numerical simulations of simultaneous and sequential movements towards the Cournot equilibrium, there is evidence of first-mover advantage. However, simultaneous movement is advantageous over sequential movement in terms of better profits for both firms and lower prices for the consumer.

Dynamic behavior in a Cournot duopoly with social responsibility

In an oligopoly with isoelastic demand, the paper analyzes the quantity competition between NPM profit-maximizing firms and NRS socially responsible firms whose objective function is a linear combination of profit and consumer surplus.From the static analysis it follows that greater social responsibility has a competitive effect, since reduces the equilibrium price and increases the market share of socially responsible firms. In addition, it increases both the consumer surplus and total surplus.For the duopoly case, the dynamic study leads to the conclusion that, if at least one of the firms follows the gradient rule as an adjustment mechanism, an increase in the speed of adjustment is a source of instability. An increase in the value of the elasticity of demand as well as a reduction in the marginal cost has a stabilizing effect on the Cournot equilibrium. A higher level of social responsibility exerts a stabilizing role on the dynamics as long as demand is sufficiently elastic.

Behavior of prosumers in Smart Grid: A comparison of Net Energy Metering and Billing Schemes, and Game Theory-based Local Electricity Market

Net energy metering (NEM) and net energy billing (NEB) are the most commonly used self-consumption schemes for prosumers in countries around the world. The concept of the local electricity market (LEM) is emerging as the potential successor of the self-consumption schemes, with several already implemented pilot projects. The comparative study of prosumers’ behavior in terms of optimal economic self-dispatching under NEM, NEB, and game-theory-based LEM energy policies is performed in this paper. The non-cooperative game-theoretic methodology is used for the calculation of Nash–Cournot equilibrium which is adopted as an LEM clearing mechanism. The prosumers’ daily energy patterns (generation, consumption, and storage) and payoffs are analyzed. Diversities of prosumers’ assets (distributed energy resources (DERs) and storage devices) and load profiles are considered. The distribution utility’s role is considered in terms of its own payoff for supplying the necessary energy to ensure the power balance equation. The numerical analysis is performed using the model of the benchmark test distribution network IEEE 33-node. The obtained results are discussed in terms of the correlation between prosumers’ behavior and the adopted energy policy. The strengths and weaknesses of the most common energy policies are highlighted from the prosumers’ perspective. The obtained results confirm that the transition from NEM to NEB self-consumption scheme could provide a better payoff to prosumers with dispatchable DERs under variable electricity price for excess energy produced. The residential prosumers equipped with SDs or dispatchable DERs were able to achieve the best payoffs in the case of Game Theory-based LEM.

Lyapunov Stability in the Cournot Duopoly Game

This paper studies Lyapunov stability at a point and its application in the Cournot duopoly game. We first explore the relationship between Lyapunov stability at a point, nonsensitivity and non-Devaney chaos and find that a dynamical system is nonsensitive and non-Devaney chaotic if there is a point in this system such that it is Lyapunov stable at that point. We next prove a group of equivalent characterizations of Lyapunov stability at a point to deduce the composite theorems and product theorems of Lyapunov stability at a point, and then we prove three equivalent characterizations of the Cournot duopoly system to demonstrate that this system is Lyapunov stable at its unique nonzero fixed point (Cournot equilibrium point) when the unit costs of the Cournot double oligarchies satisfy certain conditions. Therefore, we conclude that the Cournot duopoly system is safe relative to both sensitivity and Devaney chaos. The robustness of our results are also verified by conducting numerical simulations in the Cournot duopoly game.

A Cournot Equilibrium between Dark Net Market and Street Market

A Cournot Equilibrium between Dark Net Market and Street Market

Вероятностная модель дуополии

A probabilistic model of the duopoly market is constructed. The model is based on the assumption of the random nature of economic variables that determine the market behavior of consumers and competing firms: purchasing power; total costs associated with the production and sale of a unit of goods; commodity prices set by firms. Within the framework of the constructed model, expected values of the profit received and the amount of goods sold were found in the form of functionals of the probability density functions of purchasing power, costs, and prices for goods. Several special cases are considered when the laws of distribution of purchasing power, costs and prices are either exponential or degenerate. In each case numerical modeling was carried out, types of duopolistic relationships between the firms leading to Cournot and Bertrand market equilibria were determined, and economic criteria for the stability 
 of these duopoly market equilibria were established. It is shown that if all random variables included in the probabilistic model have exponential distribution laws, then in the duopoly market may arise an equilibrium state that is different from the Cournot equilibrium and the Bertrand equilibrium.

Strategic Investment in Power and Heat Markets: A Nash–Cournot Equilibrium Model

The current efforts to address the expansion planning of power and heat production facilities can lead to suboptimal results from a market perspective because these efforts often implicitly assume that power and heat systems are planned by a single entity. The present study addresses this issue by establishing a Nash–Cournot equilibrium model, where the producers determine the quantity of power and heat that they produce independently and simultaneously, and thereby collectively affect the price. The model considers three types of producers, including power-only, combined power and heat, and heat-only producers, where each producer determines its own expansion investment strategies independently with the aim of maximizing its own profit. An investment equilibrium is obtained by reformulating the equilibrium model as a mixed complementarity problem. Numerical results carried out on two test systems illustrate the impact of transmission congestion and supply-side market power on the investment equilibria.

Appearance of closed invariant curves in a piecewise Cournot model with advertising

In the present paper we investigate two cases which can explain what happens when the Cournot equilibrium of a duopoly model loses stability through a Neimark-Sacker bifurcation of subcritical type. This kind of bifurcation involves complex dynamics which lead to the appearance of closed invariant curves. We analyze a Cournot model where competitors hold different plants and compete on advertising quantities. The model is described by a two-dimensional piecewise map in discrete time. Making use of analytical results and numerical simulations, we show that the appearance/disapearance of closed invariant curves is directly related to two different mechanisms, namely homoclinic bifurcations and border collision bifurcations.

Market size, entry costs and free entry Cournot equilibrium

Market size, entry costs and free entry Cournot equilibrium

Cobb-Douglas Preferences and Pollution in a Bilateral Oligopoly Market

Abstract 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.

Research on the evolutionary game of knowledge pricing in an open innovation environment: from the perspective of social dual innovation balance

PurposeThis paper aims to find out the factors that influence the choice of dual innovation strategies in the process of knowledge pricing and transaction between first-mover and late-mover companies in an open innovation environment and also to find the key factors that affect the company's strategic choice in factors such as heterogeneous market environment, demand elasticity, exploration risk intellectual property prices and transaction cost.Design/methodology/approachThis study uses the Cournot equilibrium and Stackelberg two-stage master-slave game model to describe the evolutionary process of knowledge pricing in an open innovation environment of first-mover and late-mover companies.FindingsResearch shows that in an open innovation environment, the formation of a dual innovation strategy in the pricing process of corporate intellectual property transactions is a complex process. Changes in one-time transaction costs and changes in the inverse demand coefficient of the innovation market play the decisive role in the choice of dual innovation strategies. When the demand of the innovation market is moderate, the inverse demand coefficient of the innovation market and the one-time transaction cost has an inverted U-shaped influence relationship. As the innovation market's inverse demand coefficient and the one-time transaction cost increase at the same time, the degree of differentiation of the enterprise's dual innovation strategy choice gradually reduces; when the one-time transaction cost is the largest, the degree of strategy differentiation is minimized.Originality/valueBased on the above relationship, suggestions are made to guide enterprises in the knowledge pricing and transaction process in an open innovation environment, promote enterprises to form a dislocation development and complementary advantages in the knowledge innovation ecological chain and improve the overall innovation efficiency of the industry.

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

AbstractWe 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.

Stochastic planning of a multi-microgrid considering integration of renewable energy resources and real-time electricity market

This paper presents a stochastic planning algorithm to plan an operation of a multi-microgrid (MMG) in an electricity market considering the integration of stochastic renewable energy resources (RERs). The proposed planning algorithm investigates the optimal operation of resources (i.e., wind turbine (WT), fuel cell (FC), Electrolyzer, photovoltaic (PV) panel, and microturbine (MT)) and energy storage (ES). Various uncertainties (e.g., the power production of WT, the power production of PV, the departure time of electric vehicle (EV), the arrival time of EV, and the traveled distance of EV) are initially forecasted according to the observed data. The prediction error is estimated by fitting the forecasted data and observed data using a Copula method. A Cournot equilibrium and game theory (GT) are applied to model the real-time electricity market and its interactions with the MMG. The proposed algorithm is examined in a sample MMG to determine the operation of uncertain resources and ES. The obtained results are compared with a baseline and the other conventional optimization methods to verify the effectiveness of the proposed algorithm. The obtained results authenticate the importance of modeling the interaction between the MMG and electricity market, especially under the high integration of uncertain RERs, resulting in above 8% cost reduction in the MMG.

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.