Search Results (13)

The proliferation of mobile terminal applications and the increasing energy consumption of chips have raised concerns about insufficient power in mobile user terminals. In response to this issue, this paper proposes a joint optimization algorithm for UAV-assisted caching and charging based on non-orthogonal multiple access (NOMA) within the context of mobile edge caching scenarios. The proposed algorithm considers the revenue generated from UAVs providing caching and charging services to users, as well as the cost associated with leasing cache files and the UAV energy consumption. The optimization problem aimed at maximizing UAV utility is established under constraints related to power and cache capacity. To address this mixed-integer programming problem, we divided it into two parts. The first part uses the Stackelberg–Bertrand game to optimize file pricing and the UAV cache strategy. In the second part, the block coordinate descent (BCD) method is used to optimize the UAV transmission power distribution, positioning, and user pairing. The joint optimization problem is divided into three subproblems, which use the Lagrange multiplier method, a simulated annealing algorithm, and a particle swarm optimization algorithm. Simulation results demonstrate that the proposed algorithm effectively reduces user transmission delay while also improving overall revenue generated by UAVs. Full article

The Bertrand game is one of the basic game models in modern microeconomics. In some behavior experiments with game theory, it was shown that agents have different bounded rationality levels. In order to check the effect of bounded rationality levels on the stability of the equilibrium points in Bertrand games, this study establishes a new dynamic price game with a parameter to show the rationality levels. An exact geometrical characterization of the stable region of the dynamic system is firstly proposed, from which the critical points of the bifurcation of the system can be deduced. It is shown that allowing various bounded rationalities is conducive to enlarging the stable region of the equilibrium point of the price system. With increasing rationality level, the stable region expands. Numerical examples are provided to show the main results. Full article

In order to maximize benefits, oligopolistic competition often occurs in contemporary society. Establishing the mathematical models to reveal the law of market competition has become a vital topic. In the current study, on the basis of the earlier publications, we propose a new fractional-order Bertrand duopoly game model incorporating both nonidentical time delays. The dynamics involving existence and uniqueness, non-negativeness, and boundedness of solution to the considered fractional-order Bertrand duopoly game model are systematacially analyzed via the Banach fixed point theorem, mathematical analysis technique, and construction of an appropriate function. Making use of different delays as bifurcation parameters, several sets of new stability and bifurcation conditions ensuring the stability and the creation of Hopf bifurcation of the established fractional-order Bertrand duopoly game model are acquired. By virtue of a proper definite function, we set up a new sufficient condition that ensures globally asymptotically stability of the considered fractional-order Bertrand duopoly game model. The work reveals the impact of different types of delays on the stability and Hopf bifurcation of the proposed fractional-order Bertrand duopoly game model. The study shows that we can adjust the delay to achieve price balance of different products. To confirm the validity of the derived criteria, we put computer simulation into effect. The derived conclusions in this article are wholly new and have great theoretical value in administering companies. Full article

This paper investigates the competition problem between electric vehicle charging and parking desks for different owners using a non-cooperative Bertrand game. There is growing attention on electric vehicles from both policy makers and the public charging service provider, as well as the electric vehicle owners. The interaction between different entities forms a competition (game), especially between multi-type electric vehicle charging and parking facilities. Most of the existing studies on charging platforms are about the optimization of the charging platform scheduling strategy or the game relationship between charging platforms and EV users, but there is a lack of exploration on the revenue game between charging platforms. In this paper, the competitive interactions between different charging decks are studied and analyzed using a general game-theoretic framework, specifically the Nikaido–Isoda solution. In the pricing competition model, the pricing strategies of all players and physical constraints, such as distribution line capacity, are taken into consideration. Through the case studies, it is clearly indicated that the game played between different electric vehicle charging/parking decks will always converge to a Nash equilibrium point. Both charging service providers and customers could benefit from such an open and fully competitive energy service ecosystem, which enhances the overall social welfare. Full article

This paper analyzes the environmental tax’s effect on manufacturers’ choice of low-carbon technology in competitive supply chains. The existing studies only consider a single oligopoly enterprise and ignore the competition between supply chains. Few papers study the manufacturer’s technology choice under the carbon tax policy in the competitive supply chains, especially investigating the factors influencing the technology choice, including the market volume, and technology carbon emission reduction efficiency because different industry sectors have their distinctive carbon emissions reduction efficiencies and facing the different market volume. The study adopts a game theoretical approach, including the three-level supply chain consisting of the regulator, the manufacturers, and the retailers. A high carbon tax does not always help firms choose low-carbon technology. However, the monotonous effect of the carbon tax on manufacturer technology selection is no longer valid if the market volume and the carbon-reducing efficiency are considered. When the market volume is large, the regulator can set a high carbon tax to induce the manufacturers to choose low-carbon technology. We identify cases where the manufacturers are caught in a prisoner’s dilemma. When the market volume is small, and the carbon-reducing efficiency is high, the competitive manufacturers adopt the common technology. However, if the regulator increases the carbon tax, the manufacturers acquire the differential technology strategic choice, which is the Pareto optimal. We also extend the base model to the imperfect substitutable Cournot model and the Bertrand model to check the robustness and find our main results still hold in these extensions. Full article

This paper considers a Bertrand competition between two firms whose decision variables are derived from a quadratic utility function. The first firm produces new products with their own prices while the second firm re-manufactures returned products and sells them in the market at prices that may be less than or equal to the price of the first firm. Dynamically, this competition is constructed on which boundedly rational firms apply a gradient adjustment mechanism to update their prices in each period. According to this mechanism and the nature of the competition, a two-dimensional piecewise smooth discrete dynamic map was constructed in order to study the complex dynamic characteristics of the game. The phase plane of the map was divided into two different regions, separated by border curve. The equilibrium points of the map, in each region on where they are defined, were calculated, and their stability conditions were investigated. Furthermore, we conducted a global analysis to investigate the complex structure of the map, such as closed invariant curves, periodic cycles, and chaotic attractors and their basins, which cause qualitative changes as some parameters are allowed to vary. Full article

The cooperative and competitive (i.e., co-opetition) behavior between retailers plays a significant role in the development of operations and marketing strategies in a supply chain. Specifically, retailers’ co-opetition relationship pivotally influences the sustainable performance in a closed-loop supply chain. This study examines the impact of retailer co-opetition on pricing, collection decisions and coordination in a closed-loop supply chain with one manufacturer and two competing retailers. Based on observations in some industries (e.g., electronic manufacturing, fabric and textile, etc.), the cooperative and competitive relationships between retailers can be classified into the following three different modes: Bertrand competition, Stackelberg competition, and Collusion. In this paper, we establish a centralized and three decentralized game-theoretic models under these three co-opetition modes and characterize the corresponding equilibrium outcomes. The results indicate that the Bertrand competition mode yields the highest return rate, which is also superior to the other two modes for both the manufacturer and the supply chain system in terms of profitability. However, it can be shown that which mode benefits the retailers would depend on the degree of competition between the retailers and the relative remanufacturing efficiency. Interestingly, we find that the retailer’s first-move advantage does not necessarily lead to higher profits. In addition, we design a modified two-part tariff contract to coordinate the decentralized closed-loop supply chains under three different retailer co-opetition modes, and the results suggest that the optimal contractual parameters in the contracts highly rely on the remanufacturing efficiency and the competition degree between the two retailers. Several managerial insights for firms, consumers and policy makers are provided through numerical analysis. Full article

This paper tests the hypothesis that a (partial) reason why cartels—collective but costly and non-binding price agreements—lead to higher prices in a Bertrand oligopoly could be because of a selection effect: decision-makers who are willing to form price agreements are more likely to be less competitive and pick higher prices in general. To test this hypothesis we run an experiment where participants play two consecutive Bertrand pricing games: first a standard version without the opportunity to form agreements; followed by a version where participants can vote whether to have a (costly) non-binding agreement as a group to pick the highest number. We find no statistically significant difference between the numbers picked in the first game by participants who vote for and against an agreement in the second game. We do confirm that having a non-binding agreement to cooperate leads to higher numbers being picked on average. Both participants who voted for and against the agreement increase the number they pick in situations with an agreement. However, this effect is bigger for participants who voted in favour. Full article

Playing the Cournot duopoly in the quantum domain can lead to the optimal strategy profile in the case of maximally correlated actions of the players. However, that result can be obtained if the fact that the players play the quantum game is common knowledge among the players. Our purpose is to determine reasonable game outcomes when players’ perceptions about what game is actually played are limited. To this end, we consider a collection consisting of the classical and quantum games that specifies how each player views the game and how each player views the other players’ perceptions of the game. We show that a slight change in how the players perceive the game may considerably affect the result of the game and, in the case of maximally correlated strategies, may vary from the inefficient Nash equilibrium outcome in the classical Cournot duopoly to the Pareto optimal outcome. We complete our work by investigating in the same way the Bertrand duopoly model. Full article

The economic world is very dynamic, and most phenomena appearing in this world are mutually interconnected. These connections may result in the emergence of nonlinear relationships among economic agents. Research discussions about different markets’ structures cannot be considered as finished yet. Even such a well-known concept as oligopoly can be described with different models applying diverse assumptions and using various values of parameters; for example, the Cournot duopoly game, Bertrand duopoly game or Stackelberg duopoly game can be and are used. These models usually assume linear functions and make analyses of the behavior of the two companies. The aim of this paper is to consider a nonlinear inverse demand function in the Cournot duopoly model. Supposing there is a sufficiently large proportion among the costs of the two companies, we can possibly detect nonlinear phenomena such as bifurcation of limit values of production or deterministic chaos. To prove a sensitive dependence on the initial condition, which accompanies deterministic chaos, the concept of Lyapunov exponents is used. We also point out the fact that even though some particular values of parameters are irrelevant for the above-mentioned nonlinear phenomena, it is worth being aware of their existence. Full article

In the past decades, the inappropriate subsidy policies in many nations have caused problems such as serious oversupply, fierce competition and subpar social welfare in the photovoltaic (PV) industry in many nations. There is a clear shortage in the PV industry literature regarding how dual supply chains compete and the key decision issues regarding the competition between dual PV supply chains. It is critical to develop effective subsidy policies for the competing PV supply chains to achieve social welfare maximization. This study has explored the dual PV supply chain competition under the Bertrand competition assumption by three game-theoretical modeling scenarios (or supply chain strategies) considering either the public subsidy or no subsidy from a social welfare maximization perspective. A numerical analysis complemented by two sensitivity analyses provides a better understanding of the pricing and quantity decision dynamics in the dual supply chains under three different supply chain strategies and the corresponding outcomes regarding the total supply chain profits, the social welfare and the required total subsidies. The key findings disclose that if there are public subsidies, the dual PV supply chains have the strongest intention to pursue the decentralized strategy to achieve their maximal returns rather than the centralized strategy that would achieve the maximal social welfare; however, the government would need to pay for the maximal subsidy budget. Thus, the best option for the government would be to encourage the dual PV supply chains to adopt a centralized strategy since this will not only maximize the social welfare but also, at the same time, minimize the public subsidy. With a smart subsidy policy, the PV industry can make the best use of the subsidy budget and grow in a sustainable way to support the highly demanded solar power generation in many countries trying very hard to increase the proportion of their clean energy to combat the global warming effect. Several subsidy policies such as shared solar energy arrangements and performance-based incentive (PBI) are proposed to integrate the market users and the PV supply chains. This study serves as a pioneering study into the dual PV supply chain research which is very limited in the PV management and policy study literature. The findings and several untended issues provide a foundation for the future PV supply chain studies. Full article

In the study of power control and allocation based on pricing, the utility of secondary users is usually studied from the perspective of the signal to noise ratio. The study of secondary user utility from the perspective of communication demand can not only promote the secondary users to meet the maximum communication needs, but also to maximize the utilization of spectrum resources, however, research in this area is lacking, so from the viewpoint of meeting the demand of network communication, this paper designs a two stage model to solve spectrum leasing and allocation problem in cognitive radio sensor networks (CRSNs). In the first stage, the secondary base station collects the secondary network communication requirements, and rents spectrum resources from several primary base stations using the Bertrand game to model the transaction behavior of the primary base station and secondary base station. The second stage, the subcarriers and power allocation problem of secondary base stations is defined as a nonlinear programming problem to be solved based on Nash bargaining. The simulation results show that the proposed model can satisfy the communication requirements of each user in a fair and efficient way compared to other spectrum sharing schemes. Full article

This paper studies a continuous Bertrand duopoly game model with two-stage delay. Our aim is to investigate the influence of delay and weight on the complex dynamic characteristics of the system. We obtain the bifurcation point of the system respect to delay parameter by calculating. In addition, the dynamic properties of the system are simulated by power spectrum, attractor, bifurcation diagram, the largest Lyapunov exponent, 3D surface chart, 4D Cubic Chart, 2D parameter bifurcation diagram, and 3D parameter bifurcation diagram. The results show that the stability of the system depends on the delay and weight, in order to maintain stability of price and ensure the firm profit, the firms must control the parameters in the reasonable region. Otherwise, the system will lose stability, and even into chaos, which will cause fluctuations in prices, the firms cannot be profitable. Finally, the chaos control of the system is carried out by a control strategy of the state variables’ feedback and parameter variation, which effectively avoid the damage of chaos to the economic system. Therefore, the results of this study have an important practical significance to make decisions with multi-stage delay for oligopoly firms. Full article