Cournot Model Research Articles

On the stability analysis of a delayed two-stage Cournot model with R&D spillovers

We investigate the dynamics of Cournot’s duopoly model with time delays, where firms compete at the R&D level and settle on their quantity based on shared earnings at the second stage. Stability conditions of the equilibrium points and occurrence of Hopf bifurcations are analyzed. Furthermore, we present numerical simulations to furnish experimented evidence for the system’s complex behaviors.

Does the Energy Internet Improve the Efficiency of Resource Allocation? ---Theoretical Mechanism and Case Analysis

This paper analyzes the resource allocation effect of the Energy Internet through four theoretical analysis frameworks: Cournot model, time and space heterogeneity, information asymmetry, and structural upgrading. The study found that there are four path mechanisms for the Energy Internet to improve the effect of resource allocation: (1) Significantly increase the main body of energy supply and increase the level of market competition; (2) Distributed power and storage technology optimize the space-time allocation; (3) Information sharing, Reduce information asymmetry and improve the efficiency of resource allocation; (4) Advocate clean replacement and promote the upgrading of energy structure. Combining the case verification mechanism of Tianjin Sino-Singapore Eco-City, and presenting policy implications.

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.

Food Quality Competition Among Companies and Government Food Safety Supervision Under Asymmetric Product Substitution

The frequent exposures of food safety events in recent years have aroused extensive social concerns. Food quality and safety are hot topics in the food engineering field. In a market with mutual competitions, the products of different enterprises are substitutive, and enterprises have to achieve reasonable yield and to ensure product quality to maximize their profits. However, the limited production resources of enterprises affect their strategies in yield and quality. To explore enterprises’ decisions in yield and food quality under no resource constraint as well as with yield and quality under resource constraints, a Cournot model with differential product substitution was constructed by using game theory, and the effects of government monitoring on food quality decision were further investigated. Results show that enterprises with strong product substitutability increase the yield and quality of their products. They can gain higher profits under no resource constraint and under resource constraint, but their profits are lower under quality constraint compared to the profits of enterprises with low product substitutability. When the equilibrium quality of enterprises is lower than the lowest quality standard requirements of the government, a high penalty ( s ) or a relatively low government supervision difficulty ( c ) urges enterprises to improve product quality. Under this circumstance, two enterprises produce according to the lowest quality standards. On the contrary, enterprises take certain risks to produce lowquality products to increase profits. The conclusions provide a theoretical basis to formulate food safety regulation policies from the perspective of product substitutability.

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.

The Competitive Effects of Mergers with Cournot Competition

This paper provides a full characterization of the price effects of horizontal mergers in the Cournot model with heterogeneous firms and constant returns to scale. We show that the price change brought about by a merger only depends on the smaller merging firm's share and the number of firms, but is independent of the distribution of shares among other firms. Price effects are determined by factors that are either directly observable by competition authorities or can be bounded under relatively mild assumptions on demand curvature or pass-through. Estimates based on concentration measures can instead be seriously misleading. We also provide closed-form solutions for calibration that approximate merger effects on the basis of simple pre-merger parameters.

Strictly and [formula omitted]-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria

This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the Γ-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable convex optimization counterparts that have a clear-cut economic interpretation. In the case of perfect competition, this result corresponds to the two classic welfare theorems, which also apply in both considered robust cases that again yield convex robustified problems. Using the mentioned counterparts, we can also prove the existence and, in some cases, uniqueness of robust equilibria. Surprisingly, it turns out that there is no such economic sensible counterpart for the case of Γ-robustifications of Nash–Cournot models. Thus, an analog of the welfare theorems does not hold in this case. Finally, we provide a computational case study that illustrates the different effects of the combination of economic competition and uncertainty modeling.

Market power in California's water market

We estimate market power in California's thin water market. Market frictions may distort the potential welfare gains from water marketing. We use a Nash-Cournot model and derive a closed-form solution for the extent of market power in a typical water market setting. We then use this solution to estimate market power in a newly assembled dataset on California's water economy. We show that, under the assumptions of the Cournot model, market power in this thin market is limited.

A price discrimination based Cournot game model for high-speed rail and airline

This study investigates the competitive game between high-speed rail and airline on price, profit and social welfare, taking into account the airline price discrimination. We build a multi-level price competition pricing Cournot model for high-speed rail and airline to shed light on the HSR-air transport competition impact of pricing discrimination when airline could offer multi-level class seats, and analyze the optimal pricing strategy of airlines and high-speed rail operators and their impact on social welfare. The analytical results demonstrate that: airline price dis-crimination will increase social welfare and reduce consumer surplus, both airfare and airline profit increase as the degree of price discrimination increases welfare. However, HSR fare and profit decreases with the increase of the degree of price discrimination.

The stability and duality of dynamic Cournot and Bertrand duopoly model with comprehensive preference

In this paper, a Cournot model and its dual Bertrand model where firms have comprehensive preferences are developed. The preference was proposed by Bowles (2004) based on the results of Rabin (1993) and Lebine (1998). Comparable static method is used to illustrate the impact of parameters on equilibrium. Three scenarios are classified by preference parameter: completely cooperative, hostile to each other and general Cournot or Bertrand model. In each situation, Cournot model and its dual model present different chaos phenomenon which have various and abundant strange attractors, while the shapes of the stability regions are similar in the same situation. In the static setting, the local stability analysis of equilibrium gives the bounded region of quantity or price. The one-dimensional Logistic mapping is applied to studying the dynamics of the models on invariant axes. The critical curves classify different regions according to the number of preimages (q1, q2) or (p1, p2). Besides, simulations give more intuitive results: the cycle attractor, chaotic attractor and the basin of attraction with “holes” are presented. The article also provides new findings that under the assumption of comprehensive preference, the Cournot model with substitutes (complements) and the Bertrand model with complements (substitutes) are still duality models in the dynamic settings.

ELECTRICITY PRICE FORECASTING MODELS

New era has begun two decades ago in the most power sectors of the globe. As electricity itself shifted from being a commodity only to a competitive trading market instrument, forecasting of power load and prices started to be another important factor. With the introduction of liberal power markets, independent players like producers, operators, traders became an important factors of liberalized power markets. New era in this secotr also increased competition among companies and countries. Thus, as new players came into scene, electricity became to be a tradable product and similar to another commodities needs to account, forecast plan of electiricity brought new challenges. With its obstacles, new atmosphere of electiricity repormation brought benefits such as lower price to end users and more utilized energy systems among the countries. Different forecasting models have been developed in order to forsee future operations. Moreover, popular modelts from economics, such as game theories, cournot model, Bertrand model, nash equilibrium plays a big role in electricity price forecasting. Simulation modelts are another methods heavily used by producers, operators and power traders in market. Additionally, statistical models, such as moving averages, Root Mean Square Error, Mean Absolute Error, mean Absolute Percentage Error, Theil's inequality coefficient are frequesntly used to determine price movements of electiricity. As its broadly used in several different industries, Time Series models using historical information and adding updated information helps to model future movement of prices. This article discusses the several methods of price forecasting of electricity in liberal power markets as high volatility of the market raises a big risk for all participants. Forecasting models explains time series analysis and briefly discusses about autoregressive, moving average, autoregressive moving average, and seasonal autoregressive moving average models. Moreover, the article illustrates examples from electricity price and load forecasts and their comparisons with actual results from trades in Turkish electricity market.

Panel Data Analysis on the Influence of Environmental Regulations on the Inflow of Foreign Direct Investment in China

From the micro level, this paper thoroughly investigates the influence of environmental regulations (ERS) on the inflow of foreign direct investment (FDI) in China. Firstly, the entropy method was adopted to comprehensively measure the ERS intensities of 283 Chinese cities at prefecture level and above in 2003-2016. Then, the Cournot model was utilized to analyze how ERS affects FDI. After that, fixed-effects model was employed to empirically examine the impacts of ERS intensities in eastern, central, and western regions on FDI inflow. The results show that: The regression results on nationwide, central, and western samples indicate that the influence of ERS variable was significantly negative. This means ERS is indeed an important consideration of foreign investors in location selection. Besides, stricter ERS hinders the inflow of FDI, which agrees with the pollution haven hypothesis. On eastern samples, stricter ERS promotes FDI inflow, that is, the situation in eastern region meets Porter hypothesis. Finally, several suggestions were presented for policymakers based on the empirical results.

Licensing under Cournot vs Bertrand competition

In this paper we consider, on one hand, a differentiated Cournot model, and, on the other hand, a differentiated Bertrand model, when one of the firms engages in an R&D process that gives an endogenous cost-reducing innovation. The aim of the present paper is two-fold. The first is to study the licensing of the cost-reduction by a per-unit royalty and a fixed-fee in these Cournot and Bertrand models. The second is to do a direct comparison between Cournot model and Bertrand model. We analyse the implications of these types of licensing contracts over the R&D effort, the profits of the firms, the consumer surplus and the social welfare. We show that some previous results for two-part tariff licensing are not robust, in the sense that they can be not true for just either a per-unit royalty contract or a fixed-fee contract. Furthermore, by using comparative static analysis, we conclude that the degree of the differentiation of the goods assumes a great importance in the results. We also discuss the optimal licensing, meaning that which licensing method is preferred, in each of the duopoly models considered.

Stackelberg versus Cournot oligopoly with private information

We compare an n-firm Cournot model with a Stackelberg model, where n-firms choose outputs sequentially, in a stochastic demand environment with private information. The expected total output, consumer surplus, and total surplus are lower, while expected price and total profits are higher in the Stackelberg perfect revealing equilibrium than in the Cournot equilibrium. These rankings are the opposite of the rankings of prices, total output, surplus, and profits under perfect information. We also show that the first n−1 firms’ expected profits form a decreasing sequence from the first to the (n−1)st in the Stackelberg game. The last mover earns more expected profit than the first mover if n≤4, or the ratio of the signals’ informativeness to the prior certainty is sufficiently low. Lastly, there is a discontinuity between the Stackelberg equilibrium of the perfect information game and the limit of Stackelberg perfect revealing equilibria, as the noise of the demand information of firms vanishes to zero at the same rate. We provide various robustness checks for the results when the precision of signals are asymmetric, there is public information or cost/quality uncertainty, or the products are differentiated.

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.

Post-merger internal organization in multitier decentralized supply chains

This paper analyses the effects upon firms and consumers of horizontal mergers in a multitier decentralized supply chain with a finite number of players in each tier, when firms may opt for two different post-merger internal organization forms: multidivisional, in which separate divisions are kept, or traditional, with cost synergies. To this effect, we develop and solve a formal game theory-based Cournot model. The main results are: independently of the tier in which the merger takes place, higher synergies do not always lead to higher consumer welfare; despite the fact that the proposal of a traditional merger reveals significant cost savings consumer welfare may still decrease with the merger; traditional downstream mergers tend to be more profitable than traditional upstream ones; multidivisional mergers are always profitable.

Complementarities as an antitrust defense

We employ a Cournot model with interdependent demands to explore the interaction between demand and cost complementarities in mitigating upward pricing pressure, post-merger. The analysis reveals that even substantial increases in the HHI post-merger need not raise competitive concerns when output is redistributed from single-market to multi-market providers. Furthermore, the numerical simulations indicate that there is a wide range of demand and cost complementarity parameters over which even monopolization of the market would not be expected to result in higher prices. These findings may constructively inform merger policy and provide useful context for application of the DOJ/FTC horizontal merger guidelines in an increasingly digitized (network) economy.

Cournot-model-based coordinated secondary voltage control considering reactive power coupling among multiple zones

To eliminate voltage violations resulting from load disturbances, this paper proposes a coordinated secondary voltage control (CSVC) method considering reactive power coupling among multiple zones. The novelty of this method lies in solving the CSVC problem from the perspective of game theory. Specifically, the CSVC model considering coupling reactive power is described as a Cournot model, where the players are the zone controllers with the objective to minimize voltage violations, and the strategy of each zone controller is the reactive power regulation vector of the controlled generators. Thus, the Nash-Cournot equilibrium is the best control strategy of CSVC. Furthermore, the payoff function is convex, and the constraints are linear. Such a CSVC game can guarantee that the Nash equilibrium always exists and is unique. As another contribution of this work, the best response functions of each control zone are derived based on Karush–Kuhn–Tucker optimality conditions, and then the Nash-Cournot equilibrium can be found quickly by using the Newton-Raphson method to solve all the best response functions simultaneously. Computational results on the IEEE 39-bus system and a real provincial power system show the good control performance and efficiency of CSVC in terms of regulating the voltage and avoiding control oscillation.

Stability of cartels in Multimarket Cournot oligopolies

AbstractWe investigate the stability of cooperation agreements, such as those agreed by cartels, among firms in a Cournot model of oligopolistic competition embedded in a multimarket contact setting. Our analysis considers a broad array of 64 potential market structural configurations under linear demand and quadratic production costs. We establish that for an appropriate range of parameter values there exists a unique core stable market configuration in which an identical two‐firm cartel is sustained in both markets. Our result highlights the significance of multimarket presence for cartel formation in light of the well‐known result from the single‐market setting where cartels are non‐profitable.

Assessing macro-prudential policies: the case of FX lending

This paper analyzes effectiveness and side effects of pre Basel III macroprudential policy measures to reduce excessive foreign currency (FX) lending growth in Austria to the private non-financial sector. Our series of macroprudential measures were introduced in 2003, 2008, 2010 and 2013. For assessing their effectiveness, we set up a Cournot oligopoly model with two types of loans and intra-firm competition, and apply a simultaneous equation panel model to estimate the model parameters for a quarterly data set of around 750 Austrian banks from 1998 to 2016. Our results indicate that the legally binding measures starting in 2010 were more effective than previous legally non binding measures in curbing FX lending, while banks simultaneously substituting these loans with euro loans. We show that these macroprudential measures are also effective with regard to reducing the identified risks and efficiently avoid unintended negative side effects such as credit crunches.