Search Results (45)

A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms’ decisions about production levels play a crucial role in determining overall market output. Compared to duopoly models, oligopolies with more than two firms have received relatively less attention in the literature. Nevertheless, triopoly models are more reflective of real-world market conditions, even though analyzing their dynamics remains a complex challenge. A reaction–diffusion system of PDEs generalizing a nonlinear triopoly model describing a master–slave Cournot game is introduced. The effect of diffusion on the stability of Nash equilibrium is investigated. Self-diffusion alone cannot induce Turing pattern formation. In fact, linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. The conditions for the onset of cross-diffusion-driven instability are obtained via linear stability analysis, and the formation of several Turing patterns is investigated through numerical simulations. Full article

This paper studies biased-manager hiring in a market with network externalities and product compatibility. We show that the aggressivity of a biased manager has a non-linear relationship with product compatibility; however, since both owners want to hire aggressive managers, product compatibility is irrelevant to the type of manager the owner hires. In Cournot competition, product compatibility is crucial in alleviating the “prisoner’s dilemma” due to the net network effect of network externalities with product compatibility. In Bertrand competition, the “prisoner’s dilemma” is resolved when the augmented net network effect of product compatibility is large. Full article

The aggregation of ride-sharing platforms has forced traditional ride-sharing platforms to decide whether to join or leave these emerging platforms. This study presents a stylized model analyzing the demand, supply, and profit of two self-operated platforms, C2C platforms (such as DiDi and Uber) and B2C platforms, considering aggregation platform awareness and commissions. The study investigates the conditions under which the self-operated platforms should employ the entry strategy based on the optimization method and Cournot game theory, as well as exploring the reasons why self-operated platforms choose to withdraw after joining. The results show that in order to avoid competition, B2C platforms adopt an entry strategy, while C2C platforms adopt a non-entry strategy. Only during the off-peak period, when the awareness of the aggregation platform is very high and the level of competition between the two types of platforms is very intense, will both types of platforms adopt an entry strategy, but C2C platforms may experience a significant loss of market share, leading to a decline in social welfare. Furthermore, even if the self-operated platform chooses to withdraw, social welfare will still increase if the two self-operated platforms adopt the best strategy. The study contributes to sustainable development by promoting efficient resource allocation, reducing redundant competition, and improving overall market efficiency, thereby fostering a more sustainable urban transportation system. Full article

Nowadays, traffic management challenges in the era of digital transport are rising, as the interactions of various stakeholders providing such technologies play a pivotal role in shaping traffic dynamics. The objective of this paper was to present a game-theory-based framework for modeling and optimizing urban traffic in road networks, considering the co-existence and interactions of different players composed of drivers of conventional vehicles, central governing authorities with traffic management capabilities, and competitive or cooperative connected mobility private service providers. The scope of this work was to explore and present the outcomes of diverse mixed equilibrium conditions in the road network of the city of Thessaloniki (Greece), integrating the principles of user equilibrium, system optimum, and Cournot oligopoly. The impacts of varying network attributes were systematically analyzed to provide quantitative indicators representing the overall network performance. Analysis of the results provided insights into the sensitivity and the resilience of the road network under various prevalence schemes of drivers of conventional vehicles, representing the user equilibrium characteristics, or drivers relying on traffic guidance provided by a central governing authority, representing the system optimum principles as well as the cooperation and competition schemes of private connected mobility providers with certain market shares in the network. Full article

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. Full article

Competition in China’s electric vehicle industry has intensified significantly in recent years. The production mode of power batteries, serving as the pivotal component in these vehicles, has emerged as a critical challenge for electric vehicle manufacturers. We considered a system comprising an electric vehicle (EV) manufacturer with power battery production technology and another EV manufacturer lacking power battery production technology. In the context of carbon trading policy, we constructed and solved Cournot competitive game models and asymmetric Nash negotiation game models in the CC, PC, and WC modes. We examined the decision-making process of electric vehicle manufacturers regarding power battery production modes and carbon emission reduction strategies. Our research indicates the following: (1) The reasonable patent fee for power batteries and the wholesale price of power batteries can not only compensate power battery production technology manufacturers for the losses caused by market competition but can also strengthen the cooperative relationship between manufacturers. (2) EV manufacturers equipped with power battery production technology exhibit higher profitability within the framework of a perfectly competitive power battery production mode. Conversely, manufacturers lacking power cell production technology demonstrate greater profitability when operating under a more collaborative power cell production mode. (3) Refraining from blindly persisting with and advocating for carbon emission reduction measures is advisable for manufacturers amidst rising carbon trading prices. Full article

This study combines the Nash–Cournot competition model and the stochastic optimization model to examine the impact of electric vehicle (EV) quantity fluctuations on microgrid operations, aiming to optimize energy usage in a competitive electricity market. Integrating distributed energy resources and bidirectional charging, microgrids offer a novel approach for energy optimization, aiding in renewable energy generation, peak demand management, and emission reduction. Empirical evidence highlights benefits in Taiwan’s electricity market and net-zero emissions target by 2050, with a case study demonstrating enhanced local renewable energy generation due to EVs and microgrid integration. As the number of EVs increases, electricity sales from microgrids decline, but electricity purchases remain stable. The degree of electricity liberalization also influences the supply and demand dynamics of the electricity market. Microgrids selling electricity only to the main grid increases total power consumption by 65.55 million MWh, reducing the market share of the state-owned utility (Taipower). Conversely, allowing retailers to purchase from microgrids increases total consumption by 30.87 million MWh with a slight market share decrease for Taipower. This study contributes to providing an adaptable and flexible general model for future studies to modify and expand based on different scenarios and variables to shape energy and environmental policies. Full article

In the study we explore an oligopoly market for equilibrium and stability based on statistical data with the help of response functions rather than payoff maximization. To achieve this, we extend the concept of coupled fixed points to triple fixed points. We propose a new model that leads to generalized triple fixed points. We present a possible application of the generalized tripled fixed point model to the study of market equilibrium in an oligopolistic market dominated by three major competitors. The task of maximizing the payout functions of the three players is modified by the concept of generalized tripled fixed points of response functions. The presented model for generalized tripled fixed points of response functions is equivalent to Cournot payoff maximization, provided that the market price function and the three players’ cost functions are differentiable. Furthermore, we demonstrate that the contractive condition corresponds to the second-order constraints in payoff maximization. Moreover, the model under consideration is stable in the sense that it ensures the stability of the consecutive production process, as opposed to the payoff maximization model with which the market equilibrium may not be stable. A possible gap in the applications of the classical technique for maximization of the payoff functions is that the price function in the market may not be known, and any approximation of it may lead to the solution of a task different from the one generated by the market. We use empirical data from Bulgaria’s beer market to illustrate the created model. The statistical data gives fair information on how the players react without knowing the price function, their cost function, or their aims towards a specific market. We present two models based on the real data and their approximations, respectively. The two models, although different, show similar behavior in terms of time and the stability of the market equilibrium. Thus, the notion of response functions and tripled fixed points seems to present a justified way of modeling market processes in oligopoly markets when searching whether the market has reached equilibrium and if this equilibrium is unique and stable in time Full article

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. Full article

Rising fossil energy prices and the significantly decreasing prices of energy technology have resulted in electricity consumers having the option to install solar PV rooftops to rely on the self-consumption of clean energy. However, the increase in this amount is affecting the revenue of electricity as a utility, which must adapt and develop its business model to accommodate the situation. If the utility cannot be adapted in time, it may lead to a loss of income from services and the sale of electricity from fossil energy. The utility in Thailand’s electricity market that acts as the distribution system operator (DSO) is known as the Provincial Electricity Authority (PEA), and the Metropolitan Electricity Authority (MEA) is responsible for managing distribution networks and customers. There are four types of solar rooftop-as-a-service (RaaS) business perspectives they could consider as opportunities through which to minimize revenue impact. The business services were designed for the DSO customer as follows: Consulting, Design, and Installation (CDI); Operation and Maintenance (O&M); Energy Service Company (ESCO); and Power Purchase Agreement (PPA). The model comprises four customer segments: residential buildings and small-, medium-, and large-scale commercial buildings. This paper applies SWOT, Five Forces, 4P marketing, and economic impact analyses to identify the possibilities when using the DSO business model. The SWOT analysis demonstrates that ESCO and PPA are strengths in the DSO’s performance characteristics and existing customer data. In the electricity industry, both models offer enormous customer bargaining power in terms of a Five Forces analysis. The main reason is that there is currently high competition in the installation service. In the 4P analysis result, the price per unit is found to be significantly lower than in residential scenarios. Therefore, there is a format for presenting promotions with an advantage over competitors. Deploying an after-sales service that brings convenience to all customer segments is needed. The economic analysis conducted using Cournot competition game theory shows a significant differential in the Medium (M) and Large (L) customer sectors’ competition due to lower technology prices. In conclusion, with the current regulatory framework and criteria, the ESCO and PPA show the best practical model from a utility business perspective. The recommendation for DSO is to create a strategic ecosystem and to link it with private companies as their partnership business. Full article

We studied a supply chain consisting of multiple suppliers and multiple retailers. We use the Cournot–Stackelberg game, the Market–Stackelberg game, and the Market–Nash game to simulate the situation where the upstream seller’s market dominance power gradually decreases while the downstream buyer’s market power increases. The equilibrium decision and supply chain performance under the three models are compared and analyzed, as well as their responses to external market changes such as demand fluctuation and market competition intensity. The research shows that (1) in a seller-dominated supply chain, the increase in buyer power reduces market equilibrium production and wholesale price; (2) in the face of strong demand fluctuations, equivalent power between upstream and downstream can contribute to the stabilization of production and wholesale prices; (3) when market demand fluctuation is small, market power brings a higher profit level, and supply chain participants would like to actively compete for market power. However, when the demand fluctuates greatly, the profit advantage brought by market dominance is no longer significant, and there is no need to spend much to fight for market dominance; (4) the fierce competition of upstream suppliers will induce upstream to give up the competition for market dominance, and make the market power less attractive to downstream retailers. While the fierce horizontal competition downstream will stimulate both suppliers and retailers to actively compete for market power, (5) sufficient market competition will improve total supply chain profit, so encouraging competition is conducive to the overall economic development of society. Full article

This article studies the emission reduction mechanism of high-tiered carbon taxes under green and low-carbon behavior in single and two-stage supply chains. First, based on the Cournot game model, it explores the impact of high-tiered carbon tax policies on supply chain carbon reduction decisions in the green exchange market. By analyzing the effects of implementing a high-tiered carbon tax policy, the basic characteristics of its implementation are identified, and the advantages of a high-tiered carbon tax compared to a unified carbon tax are summarized. Second, it establishes a carbon reduction technology investment cost-sharing model and a carbon tax cost-sharing model under the high-tiered carbon tax policy. It analyzes and studies the impact of high-tiered carbon tax policies on balancing the relationship between members of the two-level supply chain through optimal decision-making of the two-level supply chain under two cost-sharing strategies, revealing the emission reduction mechanism of the two-level supply chain under high-tiered carbon tax policies. The results indicate that there are extreme points in the emission reduction rates of producers in the green exchange market under both the high-tiered carbon tax policy and the unified carbon tax policy. It shows that the two cost-sharing strategies can effectively alleviate the cost burden for producers, increase their marginal profits, and promote further improvement in emission reduction. It explores the emission reduction mechanism of high-tiered carbon taxes and future research should delve into the emission reduction mechanism of high-tiered carbon taxes in different carbon emission departments and regions. Full article

This paper presents a financial Stackelberg game model with two partially informed risk neutral insiders. Each insider receives a private signal about the stock value and competes with the other insider under a Stackelberg setting. Linear strategies for the game’s participants are considered and normal distributions for the fundamentals are assumed. Based on the Stackelberg game and the Backward Induction theory, the unique linear equilibrium is characterized. The findings reveal that the level of partial information might increase/decrease the insiders’ profits as well as the market parameter in the Stackelberg setting relative to the Cournot setting. Additionally, this paper considers the information sharing scenario between the two insiders competing in this Stackelberg game. The results show that multiple equilibria exist in contrast to the information sharing scenario in the Cournot game where the Nash equilibrium is unique. Full article

To address the issue of resource allocation optimization in autonomous swarm robots during emergency situations, this paper abstracts the problem as a two-stage extended game. In this game, participants are categorized as either resource-providing robots or resource-consuming robots. The strategies of the resource-providing robots involve resource production and pricing, whereas the strategies of the resource-consuming robots consist of determining the quantity to be purchased based on resource pricing. In the first stage of the game, the resource-providing robots use the Cournot game to determine the resource production according to market supply and demand conditions; in the second stage of the game, the resource-providing robots and the resource-consuming robots play the price game and establish the utility function of the swarm robots to seek the optimal pricing and the optimal purchasing strategy of the swarm robots. After the mathematical derivation, this paper demonstrates the existence of a single Nash equilibrium in the constructed game. Additionally, the inverse distributed iterative search algorithm solves the game’s optimal strategy. Finally, simulation verifies the game model’s validity. This study concludes that the designed game mechanism enables both sides to reach equilibrium and achieve optimal resource allocation. Full article

Coopetition means that in economic interactions, both competition and cooperation are presented in the same time. We built and investigated analytically and numerically game theoretic models of coopetition in normal form and in the form of characteristic function. The basic model in normal form reflects competition between firms in Cournot oligopoly and their cooperation in mutually profitable activities such as marketing, R&D, and environmental protection. Each firm divides its resource between competition and cooperation. In the model in normal form we study Nash and Stackelberg settings and compare the results. In cooperative setting we consider Neumann–Morgenstern, Petrosyan–Zaccour, and Gromova–Petrosyan versions of characteristic functions and calculate the respective Shapley values. The payoffs in all cases are compared, and the respective conclusions about the relative efficiency of different ways of organization for separate agents and the whole society are made. Full article