Search Results (50)

Demand response management (DRM) significantly influences the prospective advancement of electricity smart grids. This paper introduces three distinct game-theoretic duopoly models for the smart grid demand response management problem. It delineates several rational assumptions regarding the model variables, functions, and parameters. The first model adopts a Cournot duopoly form, offering a unique closed-form equilibrium solution. The second model adopts a Stackelberg duopoly structure, also providing a unique closed-form equilibrium solution. Following a comparison of the economic viability of the two model equilibria and an assessment of their sensitivity to parametric changes, the paper proposes a third model with a Cartel structure and discusses its advantages over the earlier models. Finally, the paper examines how demand forecasting affects the equilibrium quantities and pricing solutions of each model. 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

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. 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

In this work, we analyse a common-pool resource game with homogeneous players (both have boundedly rational expectations) and entanglement between players’ strategies. The quantum model with homogeneous expectations is a differential approach to the game since, to the best of our knowledge, it has hardly been considered in previous works. The game is represented using a Cournot type payoff functions, limited to the maximum capacity of the resource. The behaviour of the dynamics is studied considering how the fixed points (particularly the Nash equilibrium) and the stability of the system vary depending on the different values of the parameters involved in the model. In the analysis of this game, it is especially relevant to consider the extent to which the resource is exploited, since the output of the players is highly affected by this issue. It is studied in which cases the resource can be overexploited, adjusting the parameters of the model to avoid this scenario when it is possible. The results are obtained from an analytical point of view and also graphically using bifurcation diagrams to show the behaviour of the dynamics. Full article

From Cournot, Walras, and Pareto’s research to what followed in the form of marginalist economics, chaos theory, agent-based modeling, game theory, and econophysics, the interpretation and analysis of economic systems have been carried out using a broad range of higher mathematics methods. The evolution of mathematical economics is associated with the most productive and influential authors, sources, and countries, as well as the identification of interactions between the authors and research topics. Bibliometric analysis provides journal-, author-, document-, and country-level metrics. In the present study, a bibliometric overview of mathematical economics came from a screening performed in September 2023, covering the timespan 1898–2023. About 6477 documents on mathematical economics were retrieved and extracted from the Scopus academic database for analysis. The Bibliometrix package in the statistical programming language R was employed to perform a bibliometric analysis of scientific literature and citation data indexed in the Scopus database. VOSviewer (version 1.6.19) was used for the visualization of similarities using several bibliometric techniques, including bibliographic coupling, co-citation, and co-occurrence of keywords. The analysis traced the most influential papers, keywords, countries, and journals among high-quality studies in mathematical economics. 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

In this paper, we introduce a Cournot duopoly game that can characterize fierce competition in digital economies and employ it to examine the effects of research and development (R&D) spillovers while considering various competition intensities. We obtain the analytical solution of the Nash equilibrium and the expression of commodity price, firm production, and variable profit under some key competition intensities. Furthermore, we analyze the local stability of the Nash equilibrium and derive that the equilibrium may lose its stability only through a 1:4 resonance bifurcation. Numerical simulations are conducted, through which we find that the Nash equilibrium transitions to complex dynamics through a cascade of period-doubling bifurcations. Phase portraits are also provided to illustrate more details of the dynamics, which confirm the previous theoretical finding that the Nash equilibrium loses its stability through a 1:4 resonance bifurcation. Full article

With the upgrading of people’s consumption patterns, the omni-channel supply chain becomes the mainstream form of e-commerce platform enterprise development. Aiming at two different e-commerce enterprises, we construct an evolutionary game model for enterprises’ “online+offline” omni-channel construction strategy by self-build or cooperating with brick-and-mortar stores. It is based on the Stackelberg and Cournot competition model, combined with the omni-channel pricing strategy, using the theory of perfect rationality and bounded rationality, and combing the non-cooperative game and evolutionary game to realize. Moreover, the evolutionary game process is simulated. Through the dynamic changes of the system, the strategy selection behavior mechanism of the retail channel subjects is deeply analyzed. It is found that enterprises’ strategy choices are influenced by both competitors and profits, and evolutionary stabilization strategies are not unique. In addition, changes in consumer loyalty, physical feelings, and sharing ratio during the evolutionary process will affect the stability rate of enterprises’ behavioral choices. Full article

In this paper, we propose a characteristic function of the maxmax defensive-equilibrium representation that maps every TU-game with strategies to a TU-game. This characteristic function is given by a two-step procedure in which each of any two complementary coalitions successively selects the equilibrium in a way that maximizes its utility. We then investigate the properties of this characteristic function and present the relations of the cores under three characteristic functions. Finally, as applications of our findings, we provide a firm production advertising game, a supply chain network game, a cost game with strategies, and a Cournot game. Full article

This paper proposes a distributed algorithm for games with shared coupling constraints based on the variational approach and the proximal-point algorithm. The paper demonstrates the effectiveness of the proximal-point algorithm in distributed computing of generalized Nash equilibrium (GNE) problems using local data and communication with neighbors in any networked game. The algorithm achieves the goal of reflecting local decisions in the Nash–Cournot game under partial-decision information while maintaining the distributed nature and convergence of the algorithm. Full article