Cournot Model Research Articles

Quantum Cournot model based on general entanglement operator

The properties of the Cournot model based on the most general entanglement operator containing quadratic expressions which is symmetric with respect to the exchange of players are considered. The degree of entanglement of games dependent on one and two squeezing parameters and their payoff values in Nash equilibrium are compared. The analysis showed that the relationship between the degree of entanglement of the initial state of the game and the payoff values in Nash equilibrium is ambiguous. The phase values included in the entanglement operator have a strong influence on the final outcome of the game. In a quantum duopoly based on the initial state of a game that depends on one squeezing parameter, the maximum possible payoff in Nash equilibrium cannot be reached when the value of the phase parameter is greater than zero, in contrast with a game that depends on two parameters.

On Cournot and Bertrand competition in collusive mixed oligopolies

AbstractWe consider a mixed oligopoly of one public and N private firms where goods are horizontally differentiated. In our setting, an interdependent payoff structure characterizes the degree of collusion among private firms. We show that, whereas in the Bertrand model, private firms are willing to collude as much as possible, in the Cournot model, the existence of a public firm reduces the scope of collusion. We also prove that the classic discussion comparing price and quantity competition crucially depends on market collusion. More precisely, price competition unambiguously yields larger profits for private firms only if collusion is high enough. In an infinitely repeated game, we prove that collusion is easier to sustain in a larger oligopoly because, in this case, a larger N helps mitigate the effect of the public firm on private firms’ collusion sustainability. Finally, we also find that collusion is always more easily sustained in the Bertrand case than in the Cournot case.

Dynamic Investigations of Shared Bicycle Operators’ Competition Based on Profit Maximization

With the rise of the sharing economy, shared bicycles have become an important component of urban transportation. This paper explores the nonlinear dual oligopoly system for the Cournot model in the bike-sharing market; both operators have maximized profits as their competitive goals. The analysis of pivotal factors influencing passenger preferences, including pricing discounts and comfort levels, is meticulously depicted by a bifurcation diagram. A new chaotic attractor—the shared bicycle attractor—is discovered. The research results indicate that larger discounts and adjustment speeds can cause the system to be in a chaotic state, which is not conducive to the long-term development of operators, although discounts can indeed attract more passengers to a certain extent. On the other hand, the increase in the marginal cost of comfort loss can also make it difficult for enterprises to operate, which requires continuous technological innovation to improve the comfort of cycling.

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.

Effects of high-speed rail on intercity travels, utility and social welfare in urban agglomerations: A game-theoretic perspective

This paper investigates the effects of newly built high-speed rail on urban performances in terms of intercity travels, utility and social welfare by extending the two-city system into a representative urban agglomeration system consisting of a hub city and two peripheral cities. A framework based on the Cournot model with three interacted games is developed to characterize competitions among HSR operators in the system. Introducing HSR between peripheral cities decentralizes the intercity travel demands from the hub city to peripheral cities, and it does not always induce more that for the urban agglomeration. We find that “weight” on social welfare, substitutability, gross benefits ratio, HSR accessibility and frequency would differentially impact the hub and peripheral cities. Numerical examples and a case study incorporating all factors based on Central Plains Urban Agglomeration in China are conducted to illustrate the model, together with some policy implications.

Rare earth recycling and remanufacturing: Impacts on oligopoly markets and industry development from a closed-loop supply chain perspective

The recycling of rare earth elements (REEs) yielded a dual benefit by alleviating supply constraints and contributing to environmental preservation. Independent recyclers (IRs), upon extracting REEs from waste materials, not only supplied the recovered REEs to the REE conglomerates but also engaged in competitive relationships by remanufacturing REE products. This study established a closed-loop supply framework, allowing the IR flexibly to choose between remanufacturing or direct sales strategies. Using the Cournot model under inequation constraints and real market data, to explores the impact of REE acquisition prices and recycling technologies on the closed-loop supply chain (CLSC) and society. The results indicated that: (1) The recycling mode and technology do not affect market share. Compared to the IR, REE conglomerate exhibit significant monopolistic advantages, occupying at least 85.1% of the market share, which can increase to a maximum of 98% as acquisition prices rise. (2) The acquisition price of recycled REE has an “inverse U-shaped” relationship with the profits of REE conglomerate and a positive relationship with the profits of IR. (3) The recovery rate is negatively related to the profits of REE conglomerate and positively related to the profits of IR. Increasing the REE recovery rate will enhance the profitability of the IR. (4) In terms of social effects, higher acquisition price of recycled REE continuously reduce consumer surplus and social welfare. Although the REE recovery rate does not affect consumer surplus, it has a significant positive impact on social welfare.

Research on Division of Labor Decision and System Stability of Swarm Robots Based on Mutual Information.

In rational decision-making processes, the information interaction among individual robots is a critical factor influencing system stability. We establish a game-theoretic model based on mutual information to address division of labor decision-making and stability issues arising from differential information interaction among swarm robots. Firstly, a mutual information model is employed to measure the information interaction among robots and analyze its influence on the behavior of individual robots. Secondly, employing the Cournot model and the Stackelberg model, we model the diverse decision-making behaviors of swarm robots influenced by discrepancies in mutual information. The intricate decision dynamics exhibited by the system under the disparity mutual information values during the game process, along with the stability of Nash equilibrium points, are analyzed. Finally, dynamic complexity simulations of the game models are simulated under the disparity mutual information values: (1) When ν1 of the game model varies within a certain range, the Nash equilibrium point loses stability and enters a chaotic state. (2) As I(X;Y) increases, the decision-making pattern of robots transitions gradually from the Cournot game to the Stackelberg game. Concurrently, the sensitivity of swarm robotics systems to changes in decision parameter decreases, reducing the likelihood of the system entering a chaotic state.

Does financialization inhibit enterprise innovation? Analysis of innovation behavior of Chinese enterprises based on evolutionary game

Enterprise innovation remains a cornerstone of economic development, with the direct influence of financialization on enterprise innovation standing as a critical factor. In contrast with the existing research, this study constructs an evolutionary game model by utilizing the Cournot model to analyze the innovation behavior of enterprises, and analyzes the influence of financialization on enterprise innovation by incorporating investment returns, market competition, and demand scale into the research framework. In addition, this study selects the sample of the Chinese non-financial listed enterprises and using panel data for the period 2009 to 2021. Based on the findings from the empirical analysis, this study reveals that excessive financialization hinders innovation in Chinese enterprises. Additionally, an intermediary pathway involving 'financialization - investment returns - enterprise innovation' is identified as a transmission mechanism. The demand scale generated by innovation inversely correlates with the inhibitory effects of financialization on enterprise innovation behavior. Meanwhile, heightened market competition amplifies the inhibitory influence of financialization on innovation. This study provided valuable empirical evidence, facilitating the enhancement of enterprise innovation efficiency.

A dynamic surge pricing model throughout product lifecycle

The shorter lifecycle and faster upgrading of the product make the potential demand change rapidly, thereby pricing based on market changes is critical to increasing profits. In response to changes in the potential demand, we present a dynamic surge pricing model that characterizes sales trajectories and gradient pricing. We introduce the Lotka–Volterra system to construct the sale-forecast system and prove its effectiveness in predicting the product lifecycle curve that reflects the change of the potential demand. In contrast to the linear demand function, we propose a gradient pricing mechanism based on marginal sales and total sales to describe the relationship between price and potential demand throughout the life cycle. Particularly, the dynamic surge pricing model degrades to Cournot model in the maturity phase of the market. We characterize the dynamic equilibrium and conduct the sensitivity analysis of parameters, showing that the dynamic surge pricing model outperforms Cournot model in terms of profit. A numerical example illustrates that the profit of the dynamic surge pricing model is nearly 21.82% higher than that of Cournot model.

Unintended Competition from Volume Controls: A Note on the Horne v. Department of Agriculture Decision

Abstract The U.S. Supreme Court case, Horne v. Department of Agriculture, dealt with the legality of volume controls in the raisin industry. Marketing orders and volume controls in agricultural markets have a long history in the United States and have often been used to decrease price volatility. However, some have seen these volume controls as engaging in cartel behavior. Using a Cournot model, this paper shows that volume controls used by agricultural marketing orders can be profit reducing under some conditions. If producers anticipate a restriction in the production that is allowed to go into the market on a prorated basis, initial production may increase, which can lower profits. Counter intuitively, volume controls can even increase the quantity sold in the market and lower the price.

Can consumer surplus decrease with merger efficiencies?

This paper investigates the impact of mergers on consumer welfare within a Cournot model, considering mergers driven by anticipated efficiency gains and potential post-merger entry. In this framework, we demonstrate that: (i) modest efficiencies can make both merger and entry beneficial, benefiting consumers; (ii) moderate efficiencies may deter entry, harming consumers due to the merger; and (iii) significant efficiencies may discourage entry but lead to lower prices, benefiting consumers. This result, therefore, embodies an important policy implication that assessing the overall effect of a merger on consumer surplus requires evaluating merger-specific synergies alongside the likelihood of post-merger entry.

Enhancing efficiency and reliability of multi-energy systems: A hybrid heuristic algorithm for interconnected energy hubs

In response to the escalating demand for sustainable energy solutions, the integration of diverse energy sources has gained prominence. Energy hubs, facilitating the amalgamation of multiple sources, enhance system efficiency and flexibility. Yet, coordinating the operation of such multi-energy systems remains challenging due to complexity and uncertainties, especially with renewable sources. This paper introduces a Cournot model-based approach for optimizing three interconnected energy hubs. The objective is to minimize total operating costs while ensuring reliability and efficiency. Leveraging the Cournot model, commonly employed in energy studies for competition and pricing, we capture the strategic behavior of energy hubs. The proposed solution employs a modified butterfly flame heuristic algorithm to navigate the non-linear and non-convex optimization problem, efficiently seeking global optimal solutions. Numerical experiments on a three-hub test case validate the method, demonstrating a 3.5 % reduction in total operation costs compared to the base case and over 2.5 % cost reduction for each hub. The proposed algorithm outperforms traditional methods in terms of convergence speed and solution quality, offering a promising avenue for optimizing the operation and management of multi-energy systems. In summary, this paper introduces a novel approach grounded in the Cournot model and a hybrid heuristic algorithm for optimizing three interconnected energy hubs, effectively addressing uncertainties associated with renewable sources and ensuring reliable and efficient system operation.

Optimal local content requirement under export share requirement consideration

This paper considers a Cournot model with a local content requirement and export share requirement. The analysis investigates the conditions under which the local content requirement may promote an intermediate industry and explores the optimal local content requirement and the key factors that affect it. The results show that while a small local content requirement has a promotion effect when it is first introduced, while if the local content requirement is further increased, the effect will depend on the intermediate industry's production efficiency. Furthermore, the optimal local content requirement should be higher as the domestic market expands or the export price increases. Finally, the export share requirement can be treated as a policy instrument that is supplementary to the local content requirement.

Seller promotion and competition on decentralized two-sided platforms

PurposeThis paper aims to explore the promotion decisions of heterogeneous sellers on a decentralized platform under competitive conditions and analyze how seller behaviors impact platform profit, seller revenue, buyer surplus and social welfare.Design/methodology/approachThis paper considers a Cournot model consisting of a platform charging a commission rate and two sellers with different conversion rates and browsing costs. Promotion efforts by sellers can increase traffic, but they also incur promotion costs for sellers. The sellers decide on promotion effort by weighing these two effects. The authors also explore the equilibrium when the platform charges a fixed usage fee.FindingsThe seller’s profit improves as its conversion rate increases and worsens as browsing costs increase. Also, increasing the commission rate charged by the platform makes the seller invest less in promotional efforts. Therefore, the platform must consider this trade-off to determine an optimal rate. The analysis shows that the seller with a high conversion rate and high browsing cost plays a greater role in generating more overall revenue. When the market favors such a seller, the platform tends to charge less in order not to impair its profitability.Originality/valueThis paper incorporates conversion rate, buyer’s browsing cost, unit promotion cost and the fee charged by the platform into the model to study sellers’ promotion decisions on decentralized platforms.

A study of carbon cost pass-through rate differences in the power generation industry

In the context of the operation of China’s carbon emissions trading market, carbon cost pass-through will profoundly impact the country’s power generation industry. However, the core of studying carbon cost pass-through in the power generation industry is determining the carbon cost pass-through rate (CCPTR). Based on this, this paper first takes the Cournot model as the basic principle, which analyzes the impact of different power generation enterprises’ numbers and the characteristics of electricity market demand on the carbon pass-through results. Secondly, based on the Cournot model, this paper further CCPTR under marginal cost variability. The research results show that when the demand function is linear, the larger the CCPTR, the larger the proportion of carbon cost pass-through. When the demand function is isoelastic, the smaller the CCPTR, the smaller the proportion of carbon cost pass-through.

ВЛИЯНИЕ ОЛИГОПОЛИСТИЧЕСКОЙ КОНКУРЕНЦИИ НА ЭКОНОМИКУ СТРАНЫ

This paper studies the essence and significance of one of the components of imperfect competition – oligopoly. In the course of writing the paper, the main specific features of oligopoly that distinguish it from monopoly and monopolistic competition have been identified. In addition, the main conditions of its emergence were noted, with the allocation of varieties of the category under consideration. An important place in the study was given to the main models of oligopoly, in particular: price leadership model, Bertrand model, cartel model and Cournot model. In addition, a comparative analysis was conducted to identify the positive and negative sides of the existence of oligopoly. Undoubtedly, the topic of our research is very relevant at the current stage of economic development. This is primarily due to the fact that oligopoly acts as one of the most common market structures. After all, almost all technically complex industries belong to oligopoly, in particular such industries as metallurgy, electronics, automobile manufacturing and many others.

Formation mechanism of on-grid power tariff using game model of complete information

The key to the reform of the power system is to design a fair bidding and trading system. Analyzing the transaction process of electricity price competition, suppressing market power and other unfavorable factors, and finding a perfect bidding system are the research goals of this paper. In order to study the competition in the power spot market and power contract market, this paper employs the game model of complete information and the game theory as a tool. The power spot market adopts the Market Clearing Price (MCP) settlement method, in which the power grid determines the maximal real-time price of the generator node as the MCP. The price is based on the three bidding strategy curves of the power plant. As a result, a Nash equilibrium of power plant revenue is formed. According to the Cournot model and Stackelberg model that analyze the power contract market, the long-term equilibrium price of Stackelberg model in the power contract market is higher than that of the perfectly competitive market and less than or equal to the output of perfect monopoly market. The long-term equilibrium price and output in the power contract market are both certain and stable. This paper has analyzed the static game of complete information in the power market and carried out practical application. The results show that the bidding strategies of power plants have a Nash equilibrium and they have an incentive to collude. The MCP mechanism cannot solve the problem of market power influence. The conclusion of the research provides a basis for the design of the power hybrid auction system.

Firm innovation under import competition from low‐wage countries

AbstractIn recent years, manufacturing firms in the United States have faced increasing import competition from low‐wage countries, especially China. Does this competition hurt or help firm innovation? This paper studies the effect of the surge in imports from China on innovation by US manufacturing firms. We first propose a theoretical framework that generates an inverted‐U‐shaped curve of innovation on imitation, which is based on the endogenous price elasticity of demand for the product in a Cournot model. We then take the theoretical prediction to data on publicly listed firms in the Compustat data set from 1990 to 2010. We find consistent evidence that Chinese import competition had an inverted‐U effect on firm innovation, as measured by patent counts and citation‐weighted patents. Our result suggests that when import penetration is less than 60% it positively affects firm innovation, but when it is more than 60%, this positive effect is inverted. This inverted‐U relation persists when we instrument import competition in the United States by using Chinese import penetration in the United Kingdom and when we test the robustness of the results by including sector‐specific trends. We find that the inverted‐U relationship is steeper for firms in high‐tech industries.

Tencents Success in Video Streaming: An Economic Theory-based Analysis

With the rise of internet technology and the popularity of mobile devices, the video industry has become an increasingly important part of the global entertainment landscape. This paper discusses the pricing strategy of Tencent in the video streaming industry. The paper states that Tencent has used the Bertrand Model to set prices equal to marginal costs to attract customers and expand its market share. However, in the case of Tencent Videos subscription price hike, the Cournot Model may be more applicable as the firm assumes that customers will continue to subscribe during the pandemic period. Despite the subscription price increase, the change in the price would be larger than the change in demand, leading to higher profits. The article also discusses the increase in demand for Tencent Video memberships and the factors contributing to it. From a game theory perspective, Tencent and its members can be modeled as playing a classic prisoners dilemma game. Finally, the article discusses the opportunity cost for consumers and the concerns regarding the fairness of the increase in membership fees. This paper also utilizes the SWOT analysis.

Switching to profitable outside options under supplier encroachment

In practice, manufacturers may encroach on retail markets through a variety of methods, one being through the use of an online channel direct to the consumers, called encroachment. Current research typically assumes that downstream retailers retain procurement from the encroaching supplier. In reality, however, retailers may have the option of switching suppliers after encroachment. By considering a supply chain consisting of one manufacturer and one retailer with outside options, this paper analyzes the effects of the option of switching suppliers on the supply chain players' strategic interactions under the threat of supplier encroachment. We consider that the manufacturer makes encroachment decision preceding the retailer's switch decision. We capture various outcomes of the encroachment and switch decisions by using a classic encroachment model with quantity decisions (Cournot model). Specifically, we identify two effects of the outside option on the strategic encroachment decision. The first, the deterrence effect, means that the manufacturer's encroachment is deterred by the threat of switching supplies altogether; while the second, the permissive effect, indicates that the retailer intends to switch to the alternative source after the encroachment. Interestingly, we show that the encroachment could improve the total profit of the incumbent manufacturer and the retailer even when the retailer's switch has occurred. In this case, however, the manufacturer profits while the retailer is hurt by the encroachment and the switch. Finally, we also investigate several extended cases to demonstrate the robustness of our findings.