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[Objective] In the context of promoting energy structure transformation and accelerating the construction of a new energy system, clarifying the energy input strategies and their influencing factors across different regions is of great significance for formulating region-specific energy policies and orderly advancing regional renewable energy integration. [Methods] Based on a game theory framework, this study theoretically deduced the energy input strategies and influencing factors of different regions in the context of energy structure transformation. It also conducted empirical tests corresponding to the implementation effects of wind power subsidy policies in different regions of China and the progress of renewable energy integration in Europe. [Results] (1) Under the fossil fuel energy scenario, regions exhibited non-cooperative game behavior, where regional energy input strategies were characterized by non-cooperative games, displaying path dependency and influenced by the scale of capital and labor factors in the region. (2) Under the renewable energy scenario, regions engaged in cooperative games, with energy input strategies reflecting cooperative games, influenced by the unit cost of renewable energy, the scale of capital and labor factors, and the differences in the scale of capital and labor factors within the region. (3) When there are larger disparities in the scale of capital and labor factors among different regions within an area, lower costs of renewable energy, and a higher overall scale of capital and labor factors, the area is suitable for prioritizing the renewable energy integration, which is more conducive to the orderly achievement of energy efficiency improvement and energy structure transformation. [Conclusion] Dynamically adjusting energy input strategies, emphasizing the alignment of renewable energy deployment with regional factor endowments, and leveraging the leading role of central cities are crucial strategies for promoting China’s energy structure transformation. The findings of this study provide policy insights for the orderly advancement of renewable energy integration and the construction of a new energy system.

In the context of China’s vigorous promotion of inter-provincial electricity market construction， there exists a competitive dynamic among multiple purchasing provinces participating in the inter-provincial electricity spot market. To devise a rational bidding strategy for these purchasing provinces， a game bidding model for electricity purchasing tailored to the inter-provincial electricity spot market is proposed. Firstly， the marginal inter-provincial electricity purchase quantity-price curve is calculated based on the operational conditions of the electricity market within each province， serving as the bidding curve for its participation in the inter-provincial electricity spot market. Subsequently， a model for market clearance and pricing in the inter-provincial electricity spot market is proposed under the scenario of variable flow directions of tie-lines. A non-cooperative game bidding model for the inter-provincial market， involving multiple purchasing provinces， is established， where the bidding curve obtained under Nash equilibrium represents the optimal electricity purchase bid for the purchasing provinces. Finally， a simulation calculation is conducted on a case study system comprising two selling provinces and three purchasing provinces to validate the effectiveness of the proposed model and obtain the Nash equilibrium solution of the bidding model for electricity purchase.

In this study, we deploy game theory to examine pricing competition between hospitals and pharmacies within China’s pharmaceutical supply chain. Addressing issues of drug shortages and price disparities, we construct a model featuring a single supplier, multiple hospitals, and multiple pharmacies. All retailers distribute a single type of medication and participate in competitive pricing. In this context, they must determine optimal selling prices and order quantities to maximize their market effectiveness. Hospitals receive government discounts during drug procurement and must utilize reserve warehouses for replenishment when demand exceeds supply. We establish the existence and uniqueness of the Nash equilibrium and derive closed-form solutions for exponential stochastic demands, outlining the pricing and ordering strategies of hospitals and pharmacies. Our analysis discloses that pronounced price sensitivity, reduced reliability, limited discounts, and increased wholesale prices are key contributors to drug shortages. While such shortages appear inevitable in pharmacies, mandatory replenishment mechanisms can alleviate such shortages in hospitals without necessarily escalating drug prices or impinging on hospital profits.

Transactive energy (TE) as a market-based mechanism provides a practical framework to fully manage and control local energy networks with a high penetration of distributed energy resources (DERs). However, the existing designed TE frameworks can rarely encourage prosumers to participate fairly owing to neglecting competition and cooperation. This paper proposes a tri-layer hybrid game-based TE framework, wherein the cooperation of prosumers to trade energy in a peer-to-peer (P2P) fashion is considered in the first layer using the Nash Bargaining Game (NBG) Theory. The competition among prosumers to trade with the most affordable aggregator is modeled at the second layer using the evolutionary game (EG). The third layer also models the competition among aggregators and the competition between aggregators and the cooperation of prosumers by developing a non-cooperative game. Besides, a scale-independent distributionally robust optimization (DRO) is developed based on the Wasserstein ambiguity set to allow prosumers to manage their uncertainty using all potential historical data while ensuring tractability. Finally, a new adaptive proximal alternative direction method of multipliers (ADMM) is introduced to develop a distributed-decentralized decision-making scheme for satisfying network constraints and energy trading in a P2P manner to accelerate the solution procedure and preserve privacy. The tests and implementations demonstrate that the proposed tri-layer TE framework lowered the overall costs for prosumers by 11 % and 2.85 % compared to the total costs in non-cooperative TE and cooperative TE, respectively.

Multi-energy systems are one of the key technologies to tackle energy crisis and environmental pollution. An energy hub (EH) is a minimum multi-energy system. Interconnection of multiple EHs through energy routers (ERs) can realize mutual energy assistance. This paper proposes a peer-to-peer (P2P) energy sharing strategy between EHs including ERs in an interconnected system, which is divided into two levels. In the lower level, a method of determining the charging/discharging constraints of energy storage devices is proposed. Based on the Lyapunov optimization method, virtual queues are used to model the energy storage devices and flexible loads in the system. The objective is to minimize the overall operating cost of the interconnected system. In the upper level, a non-cooperative game model is introduced to minimize the cost of purchasing power from other EHs for each EH. A best response-based method is adapted to find the Nash equilibrium. The simulation outcomes demonstrate that application of the proposed strategy can reduce operating costs of an interconnected system and each EH. On basis of a real-world dataset of interconnected EHs, both analytical and numerical results show the effectiveness of the proposed strategy.

In order to solve the spectrum efficiency optimization problem of device-to-device (D2D) communication in many-to-one reusing mode, the channel allocation and power control problem in the frequency-selective channel environment is investigated. A resource allocation algorithm based on hierarchical optimization is proposed. The highly coupled resource allocation problem is decoupled by introducing the layering idea. Firstly, in the outer layer, a power control algorithm based on discrete power selection and two fast channel allocation algorithms based on priority setting are proposed. By using discrete power control for cellular users, the problem of multiple local optimal solutions is solved, which makes the power control algorithm of the whole system converge. Meanwhile, the proposed channel allocation algorithm reduces the complexity by setting priorities for D2D users, and at the same time realizes the suppression of cross-layer interference. In the inner layer, a resource allocation algorithm based on a non-cooperative game is proposed. By modeling D2D users share the same channel as a non-cooperative game model and introducing the cost function in term of same-layer interference, it achieves the suppression of same-layer interference while improving the spectrum efficiency. And the Nash equilibrium solution of the game is obtained by solving the KKT condition. Simulation experiments show that the proposed algorithm not only improves the spectrum efficiency of the system compared with the existing algorithms, but also proves the superiority of the algorithm in ultra-dense D2D communication scenarios.

The Paris Agreement, which is carried out in a bottom-up manner, is giving great vitality to the transition to low-carbon energy system. Accordingly, as the spread of renewable energy increases, securing flexibility resources is emerging as a keyword in the power system and power market, and many studies on demand response (DR) and energy storage system (ESS) classified as demand-side flexible resources are being conducted. However, most of the studies on DR are on voluntary DR programs that participate through bidding among incentive-based DR or price-based DR programs, and ESS faced difficulties in its distribution due to low economic feasibility. Therefore, in this work, we propose a feasible process for participating in a reliability DR program that guarantees high profitability but involves high uncertainty, and non-cooperative game model is suggested to mitigate the uncertainty through surplus electricity-trading model of ESS. In addition, a subjective decision-making based on prospect theory is proposed to reflect the impact of the uncertainty about the incentive-based program’s engagement. Case study results performed in an environment formed based on actual operation data of the Korean DR market prove that participants’ uncertainty is mitigated when participating in the DR market through power trading of ESS through the proposed model. In addition, a small-scale ESS with an average benefit–cost ratio of 0.78 improves by up to 1.08 (1.04 with a standard scenario).

“Sharing economy” refers to a transformative socio-economic phenomenon where individuals or institution with idle resources transfer the right to use resources for economic compensation. With the widespread adoption of distributed photovoltaic generation and energy storage (ES) device in residential communities, there is a growing interest in establishing a suitable platform for residential users to share their ES capacity with community shared equipment controllers (CSECs). This paper proposes a local ES capacity sharing market, and presents the market trading process, pricing and allocation rules using an iterative uniform-price bidding mechanism Acknowledging the selfish-interest of both RUs and CSECs, we introduce the resource management organization (RMO) as a regulated third-party organization responsible for administering the market. To evaluate the proposed scheme, we conduct case studies based on real-life data from Pecan Street. The numerical experiment results demonstrate the effectiveness and applicability of our approach.

Exchange rate and its related risk management are too important for main participants in foreign exchange markets. There are many approaches developed in the literature for studying risk management say arbitrage detection, say finding replication portfolio. However, in the current paper, arbitrage opportunities are studied using the game theory perspective. This paper proposes different types of games played in a specified foreign exchange market in the presence of three exchange rates. Proposed games are exchange rate games in two cases of no arbitrage and existence of arbitrage, optimal stopping game, the arbitrage game, threshold strategies used in global game and Non-cooperative exchange rate game. Most of cases, the bang-bang rule of optimal control is used for finding the Nash equilibriums (NE). However, simulated and stochastic approximation (SA) solutions are also given. Most highlights of the current paper are: (I) considering two types of arbitrage opportunities, simultaneously, (II) translating arbitrage detection as game theory concepts, (III) solving the problem using techniques of optimal control theory. Finally concluding remarks are proposed.

ABSTRACTLocal governments often provide tax-subsidy programs to attract corporate investment. Using a game-theoretic real options model between a firm and a government, this paper aims to explore the interaction between the government’s tax-subsidy policy and the firm’s investment and financing decisions. The optimal incentive policies are derived for cooperative and non-cooperative bargaining settings between a government and a firm. We show that it is optimal for the government to offer a tax-subsidy combination in the cooperative setting. However, this is not true for the non-cooperative setting, in which the optimal policy is to only levy taxes with no investment subsidy. Whereas firms always have an incentive to rely on debt financing in the non-cooperative setting, firms are reluctant to issue debt in the cooperative setting. Finally, it is generally optimal for the government to collect taxes at a lower rate in the case of high risk high-tech enterprises.

In this article, a distributed charging strategy problem for plug-in electric vehicles (PEVs) with feeder constraints based on generalized Nash equilibria (GNE) in a novel smart charging station (SCS) is investigated. The purpose is to coordinate the charging strategies of all PEVs in SCS to minimize the energy cost of SCS. Therefore, we build a non-cooperative game framework and propose a new price-driven charging control game by considering the overload constraint of the assigned feeder, where each PEV minimizes the fees it pays to satisfy its optimal charging strategy. On this basis, the existence of GNE is given. Furthermore, we employ a distributed algorithm based on forward–backward operator splitting methods to find the GNE. The effectiveness of the employed algorithm is verified by the final simulation results.

This study investigates the dynamics of endogenous order placement timing among competing retailers within a single period, driven by the evolution of demand-forecast information. Despite the critical role of accurate market trends and demand forecasts in determining firm success during selling seasons, the existing literature lacks a comprehensive understanding of how firms strategically adjust their order timing with imperfect and evolving information landscapes. By leveraging resources such as predictive analytics systems operated by big data and social media, firms tend to enhance their market demand precision as the selling season approaches, aligning with market practices. With this background, we aim to address the strategic behaviors of competing retailers in timing their orders, filling the aforementioned research gap. We construct a non-cooperative game-theoretical model to analyze the strategic behaviors of competing retailers in timing their orders. The model incorporates factors such as imperfect and evolving information landscapes, considering how firms leverage resources to enhance their market demand precision as the selling season approaches. Our analysis shows two primary equilibria, each shedding light on distinct strategic choices and their implications. First, the better-informed firm decides to execute early orders, capitalizing on the first mover’s advantage, particularly when initial information imprecision exceeds a specific threshold. Conversely, a second equilibrium emerges when the better-informed firm delays its orders, yielding the first mover’s advantage to the less-informed competitor. These equilibria highlight the correlation between order timing strategies and the trajectory of information evolution within the competitive landscape. Additionally, our study extends beyond equilibrium analysis to investigate these strategic choices on supply-chain performance.

To address the safety and efficient driving issues of human–machine shared control vehicles (HSCVs) in future complex traffic environments, this paper proposes a game theory-based interactive control method between HSCVs and surrounding autonomous vehicles (SVs) and involves considering different driving behaviors. In HSCV, a comprehensive driver model integrating steering control and speed control is designed based on the brain emotional learning circuit model (BELCM), and the control authority between the driver and the automation system is dynamically allocated through the evaluation of the driving safety field. Factors such as driving safety and travel efficiency that reflect personalized driving style are considered for modeling the uncertain behavior of SVs. In the interaction between HSCVs and SVs, a method based on game theory and distributed model predictive control (DMPC) that considers the uncertainty of SVs’ driving behavior is established and is finally integrated into a multi-objective constraint problem. The driver control input in an HSCV will also be introduced into the solution process. To demonstrate the feasibility of the proposed method, two test scenarios considering the driving characteristics of different SVs are established. The test results show that automation control systems can promptly stop the human driver’s dangerous operations in an HSCV and safely interact with multiple AVs with different driving characteristics.

Rate-Splitting Multiple Access (RSMA) has recently found favor in high-mobility scenarios due to the benefits of relaxing the accuracy of Channel State Information at the Transmitter (CSIT) while maintaining high spectral efficiency. These benefits are particularly important in Satellite-Vehicular Networks (SVNs), where the mobility of the vehicles significantly affects the estimation accuracy of the CSIT. To tackle this challenge, we propose an RSMA-based satellite-vehicular communication system for reliable data transmission. Specifically, we investigate the outage probability of the RSMA-based satellite-vehicular communication system under the Shadowed-Rician model. Considering the satellite-vehicular communication outage problem, an optimization problem is formulated to maximize the Weighted Sum Rate (WSR) of the communication system. However, due to communication overhead and privacy concerns, not all vehicles are willing to participate in interference management. In this study, we exploit an incentive mechanism to efficiently solve this problem. Specifically, we formulated a non-cooperative game to motivate users to report the CSIT and participate in the power allocation. In addition, we have proved the existence and uniqueness of Nash Equilibrium (NE) in the game formulated. Our simulation results show that the proposed non-cooperative game theoretical approach achieves the effectiveness of the RSMA-based satellite-vehicular system. The game theoretical framework is shown to motivate users to participate in interference management, so as to maximize their transmission rates.

Since the number of electric vehicles (EVs) grows rapidly, the EVs charging schedule problem has attracted more attention than before. On account of continuous and random power requirement from EVs, the burden of grid will increase and thus jeopardize the stability of grid. In this paper, an accessible close-loop vehicle-to-vehicle (V2V) charging mechanism with interaction of energy and information under charging station is proposed to cope with EVs charging schedule problem. And the non-cooperative game model is adopted to analyze the V2V charging mechanism. Furthermore, the optimal strategy algorithm is introduced to get the Nash Equilibrium (NE) of the game. Simulation with 10 EVs illustrates that V2V charging with non-cooperative game can decrease the load variance (0.0701) compared to V2V charging without the game (1.7248). And the convergence of the optimal strategy algorithm can reach in less than 20 iterations.

The Multiple Microgrid System (MMG) facilitates synergistic complementarity among various energy sources, reduces carbon emissions, and promotes the integration of renewable energy generation. In this context, we propose a two-stage robust cooperative scheduling model for MMGs based on non-cooperative game theory and a benefit allocation mechanism. In the first stage, considering electricity price fluctuations and uncertainties in wind and solar power outputs, a robust optimization approach is applied to establish an electric energy management model for MMGs. This model enables point-to-point energy sharing among microgrids. In the second stage, addressing the benefit allocation problem for shared electric energy, we introduce a Cost Reduction Ratio Distribution (CRRD) model based on non-cooperative game theory. The generalized Nash equilibrium is utilized to determine the benefit distribution for shared electric energy. Finally, through case studies, the proposed model is validated, ensuring fair returns for each microgrid. The results indicate that the proposed model optimizes the operational states of individual microgrids, reduces operational costs for each microgrid, and lowers the overall total operational costs of the MMG system. Additionally, an investigation is conducted into the impact of electricity price uncertainty coefficients and confidence levels of wind and solar uncertainties on the operational costs of microgrids.

The capacity optimization and allocation of hybrid microgrid with multiple distributed generations is an important aspect of microgrid design. The capacity allocation problem of the integrated microgrid system involving wind farm,photovoltaic power station and hydrogen production-hydrogen storage-power generation system is studied in this paper. Firstly,three investors of wind power,photovoltaic and hydrogen generation-hydrogen storage-power generation system are established,and the optimal allocation model of wind-photovoltaic-hydrogen microgrid capacity based on non-cooperative game is established with the goal of maximizing the profit of each investor. Secondly,considering economic factors such as investment cost,operation and maintenance cost,power purchase and sale cost,wind and light abandonment penalties and load interruption penalties of each game player,the capacity allocation of participants in the game is optimized individually using the particle swarm algorithm. Meanwhile,the Nash equilibrium point that maximizes the revenue of each game player is determined. Finally,the wind speed and light intensity data of a typical month in the region of Xinjiang is used for the arithmetic analysis of the microgrid capacity configuration. The results show that the model can ensure the reliability of power supply with relatively low monthly integrated cost and realize the reasonable allocation of microgrid system capacity.

A vehicular fog network is an emerging paradigm adopted to facilitate delay-sensitive and innovative applications. Since vehicular environments are inherently dynamic, it becomes a challenge to effectively utilize all available resources. Often a centralized resource distribution model is adopted for effective resource utilization but this comes with significant overhead. Thus, a distributed model seems more suited for highly dynamic vehicular environments; however, a distributed model without collective intelligence can end up in uneven workload distribution. In this paper, we propose a distributed non-cooperative task offloading framework for efficient resource utilization. Here, vehicles with heterogeneous task requirements interact with one another without directly influencing the actions of the neighboring vehicles. That is, the framework allows vehicles to communicate with neighbors to gather contextual information to revisit their offloading decisions. The shared information includes resource type, task residence time, system cost, and offloading inference. The effectiveness of the framework is evaluated against baseline schemes in terms of service delay, transmission delay, system cost, delivery rate, and system efficiency. The results demonstrate significantly reduced task residence times by 50%, highest throughput at 83 Mbits/s, which in turn contributes to an improved system utilization up to 70% across the resource-sharing network.

In the context of global efforts to develop low-carbon economy and curb the growth of fossil energy, it is particularly important for supply chain enterprises to make scientific decisions on emission reduction and energy conservation. This paper investigates supply chain enterprises to make emission reduction decisions by considering cost-benefit of carbon emission reduction and internal and external factors changes. We analyze the dynamic game model of a three-level supply chain consisting of suppliers, manufacturers, and retailers in cooperative and non-cooperative states. The change of optimal emission reduction is calculated by differential game and dynamic analysis. The optimal profit is obtained from the corresponding optimal decision of enterprises, and the optimal proportion of manufacturers’ share of emission reduction cost is studied. We adopt numerical simulation method to simulate decision-making evolution process of emission reduction. Finally, the impact of different influencing factors on product emission reductions, supply chain decisions and profits are shown. These findings can provide theoretical support and reference for multi-level supply chain decision-making.

Demand response (DR) with the participation of load aggregator (LA) has received extensive attention in recent years due to the increasing energy demand. However, LA has to face the risk that consumers may refuse to be controlled by LA due to the uncertainty of energy consumption on demand side. Therefore, this paper proposes a joint game-theoretical optimization for LAs in DR day-ahead market and intraday market considering the breach of residential consumers. In day-ahead market, LA will compete with other LAs and obtain the optimal bidding amount through a non-cooperative game process, to obtain the maximal self-profit. In intraday market, in order to make up for the breach amount of consumers, DR resource-deficit LAs can purchase resource from DR resource-surplus LAs via Nash bargaining process. Basically, Nash bargaining model is formulated and solved by translating the optimization problem into two sub-problems. Finally, a case study is performed to show the effectiveness of the proposed DR framework. Simulation results show that the whole profit of all LAs increases 25.9% compared with the scenario where LAs only participate in day-ahead market and will be punished by DR market due to the bidding breach.

In this paper, a hybrid differential evolution particle swarm optimization (PSO) method based on a good point set (GPDEPSO) is proposed to compute a finite noncooperative game among N people. Stochastic functional analysis is used to prove the convergence of this algorithm. First, an ergodic initial population is generated by using a good point set. Second, PSO is proposed and utilized as the variation operator to perform variation crossover selection with differential evolution (DE). Finally, the experimental results show that the proposed algorithm has a better convergence speed, accuracy, and global optimization ability than other existing algorithms in computing the Nash equilibrium of noncooperative games among N people. In particular, the efficiency of the algorithm is higher for determining the Nash equilibrium of a high-dimensional payoff matrix game.

With the acceleration of China’s electricity market construction, it is urgent to establish a unified electricity transaction mechanism to balance the interests of all parties and build a competitive electricity market. Game theory has significant advantages in the study of decision optimization among multiple decision-making bodies that interact and compete with each other. Therefore, the application of game theory in the electricity system has attracted the attention and research of a large number of scholars, among which the research on the electricity market accounts for the highest proportion. In this study, the concept and evolution of cooperative game theory, non-cooperative game theory, and evolutionary game theory in game theory are described in detail. Second, the status quo and scale of the domestic and foreign electricity market are sorted out and summarized. Finally, according to the research results of the application of three kinds of game theory in the electricity market in recent years, this study evaluates and analyzes the three typical aspects of the power generation side, the power sale side, and the power consumption side, and puts forward the prospect of the application of game theory in the electricity market in the future.

This paper investigates a possible future business case for green hydrogen production from hydropower. The main research question is to find the trade-offs for a run-of-river hydropower plant owner between the currently prevailing business model of wholesale electricity trading and, alternatively, production of green hydrogen. Hence, a bi-level optimization framework between a hydropower plant owner (H2 producer and price setter) and a transportation firm (H2 consumer) is developed. The empirical scaling of the numerical example describes Central Western European wholesale electricity market settings. Results indicate that the current market environment and price setup do not allow for profitable green hydrogen production as yet. However, an increasing CO2 price as the key determining parameter leads to improved competitiveness and expected profitability of the business case studied in this work. In the numerical example examined, a CO2 price above 245EUR /t triggers profitability, when green hydrogen production is competing with a future electricity contract price of 45EUR /MWh.

Eco-compensation is an important policy tool to trade off economic development and environmental protection in a watershed. This study introduced the gross ecosystem product (GEP) accounting system to identify the eco-compensation provider (ECP) and eco-compensation receiver (ECR) of a river basin. Then, a cooperative game model and a non-cooperative game model between the ECP and the ECR were established, in which system dynamics was incorporated into the game theoretical analysis to aid selection of the optimal compensation scheme. The study further demonstrated the model applications by taking the Tuojiang River Basin as a case. The results showed that the accounted GEP increased from CNY 32.2 billion in 2018 to CNY 35.5 billion in 2020, with a growth rate of 10.2%. Deyang City, as an ECP, had a cumulative difference of CNY 11.759 billion between its accounted GEP and actual GEP output over the three years. Neijiang City, Zigong City, and Luzhou City were taken as the ECR, receiving the GEP revenues as CNY 11.289 billion, 7.661 billion, and 1.497 billion, respectively. Chengdu City changed from the ECP to the ECR and ultimately to the ECP. However, Ziyang City and Meishan City changed from the ECP to the ECR. The eco-compensations increased to varying degrees during 2018–2020 in both game scenarios, with ECP payments and ECR revenues increasing by 16.5% and 4.6% in the non-cooperative game and by 5.0% and 50.8% in the cooperative game. Particularly, the eco-compensation obtained by the cooperative game had better environmental and economic performance, as there was a total of CNY 7.049 billion being saved. However, there was no savings of compensation by the non-cooperative game. It is expected that the results may provide insight into the design of the eco-compensation standard for a river basin.

In this paper, a modified distributed Nash equilibrium seeking problem with input saturation has been investigated. The payoff function of each player is related to the communication topology, which is closer to the actual scenes. The sigmoid function is utilized to limit the range of the input. Through the network communication between players and the gradient of the players’ payoff functions, the finite-time and fixed-time distributed Nash equilibrium seeking protocols with input saturation are given. Using the Lyapunov stability analysis, it is determined that the action of each player converges to the Nash equilibrium if all the players update their action according to the proposed algorithms. The numerical simulations are also provided to testify the algorithms.

Abstract In this paper, we proposed a novel power allocation algorithm based on hierarchical game in 5G heterogeneous integrated networks. The radio network controller is the first layer, the base stations are the second layer, and the base station users are the third layer. The stackelberg game model is used between the first and second layers, in which the radio network controller is the leader and the base stations are the followers. The radio network controller sets the interference prices for the base stations and the users in the third layer can update their transmission power by non-cooperative game based on the setting interference price. According to the proposed scheme, the users power allocation can reach the Nash equilibrium through by non-cooperative game and obtain the optimal transmission power. Moreover, it is proved that the equilibrium solution is composed of the optimal price and the optimal transmission power, and the convergence of this algorithm is also verified. The simulation results show that the proposed algorithm can decrease the interference and improve the system capacity.

The paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.

This paper focus on the two-tier downlink heterogeneous networks (HetNets) with non-orthogonal multiple access (NOMA). The aim is to jointly optimize user scheduling and power allocation to solve the problem of maximizing the energy efficiency (EE) of the NOMA HetNets. We formulate the basic principle of NOMA and develop the EE model of joint user scheduling, optimal power allocation factor among users on the same subchannel and power allocation across subchannels. Firstly, considering that the problem of formulation is a multi-objective optimization (MOO) problem, which is non-convex and NP-hard, we decouple the MOO problem into two single-objective optimization (SOO) problems: 1) joint the optimal power allocation factor of maximizing the EE among users on the same subchannel to solves the subchannel matching, and 2) the power allocation across subchannels. For subchannel matching, non-cooperative game and global optimal search (GOS) are respectively used to solve the power allocation factor among users on the same subchannel and user scheduling. For the power allocation factor among users on the same subchannel, the existence of Nash equilibrium (NE) is proved by introducing super-modular game. Besides, the Nash equilibrium point (NEP) of the game can be obtained by using the proposed algorithm. Then, for the correlation between users-subchannels, this paper proposes a non-cooperative game based user-subchannel global optimal search matching algorithm (NCG-US-GOSMA) with low-complexity. Finally, according to the obtained subchannel matching, the non-convex problem of power allocation across subchannels is converted into convex problem by successive convex approximation (SCA), and then solve it by iteration. Simulation results verify the effectiveness of the proposed scheme; in addition, the EE performance is better than the existing resource allocation algorithm and OFDMA scheme.

Energy efficiency (EE) optimization is investigated for a multi-user cognitive radio network (CRN) over multiple-input-multiple-output (MIMO) interference channels (ICs). To reduce the system overhead due to information exchange among the secondary CR uses (SUs), the EE optimization problem is formulated as a non-cooperative game, where each SU transmitter competes against the other SU pairs by optimizing its transmit covariance matrix. Specifically, each multi-antenna SU maximizes locally its energy efficiency in terms of the number of bits transmitted per unit energy consumption, subject to the per-SU transmit power constraint and the primary user (PU) perceived total interference constraint. It is proved that the formulated non-cooperative game admits at least one Nash equilibrium (NE), and the sufficient condition for a unique NE is derived subsequently. Primal decomposition is employed in the local EE optimization problem to relax the coupling PU perceived interference constraint such that fully distributed operation is allowed. A distributed iterative EE optimization algorithm (DIEEOA) is then proposed to obtain the unique NE, which is shown to converge to the global optimum. Linear precoding techniques are employed to mitigate the impacts of multi-user interference and imperfect channel state information (CSI). Through numerical simulations, effectiveness of the proposed scheme is validated and the system setting parameters' impacts on the performance are studied.

Developing a reasonable, efficient distributed market transaction mechanism is an important issue in distribution systems. The gaming relation between distributed transaction market entities has yet to be fully elucidated in various trading links, and the impact of distributed transactions on distribution network operations has yet to be comprehensively analyzed. This paper proposes a novel distributed Peer-to-Peer (P2P) day-ahead trading method under multi-microgrid congestion management in active distribution networks. First, a flexible load model for price-based demand response load and an autonomous microgrid economic scheduling model are constructed. Second, under normal operation of the distribution network, a non-cooperative game model and Stackelberg game model are employed to separately and comprehensively analyze gaming relationship among sellers, and between sellers and buyers. Thereafter, a congestion management method based on market capacity is established from the perspective of distribution network control centers. Finally, the impact of end energy consumption characteristics on microgrid economic scheduling and P2P trading is analyzed through a modified IEEE 33-node power distribution system. The economic and technical benefits such as congestion mitigation and network loss reduction that produced by P2P trading to the operation of microgrid systems are analysed with specific indicators.

For the redundancy coverage of nodes leads to the phenomenon of low energy efficiency,Non-cooperative game theory was used to solve it.A revenue function was proposed,which considering the coverage of nodes and the residual energy.The lifetime of the node and network path gain were applied to revenue function.The network topology was built by nodes with the appropriate work strategy.Control algorithm coverage in wireless sensor network was proposed based on Non-cooperative game theory.A Nash equilibrium between the coverage rate and the residual energy was proved,and the return function converged to the Pareto optimal.Experiments show that the algorithm can provide reasonable coverage of network nodes and ensure energy efficiency.

With the aggravation of global environmental problems, energy saving, and emission reduction are urgent for the manufacturing industry. However, due to the difficulty in coordinating the manufacturing behaviors and profit targets of different subsidiaries, the large complex product manufacturing group is difficult to transform from traditional profit-oriented to green-oriented. To this end, this paper proposes two production planning optimization strategies for the manufacturing group. One is the profit-optimized strategy that optimizes the cost and makespan of the group manufacturing process. The other is the energy-optimized strategy that adds the energy consumption objective to the group's original objectives. Meanwhile, the potential benefit conflict of different strategies is considered in this paper. The non-cooperative game is introduced to analyze the benefit allocation under the two strategies and formulate a reward mechanism to encourage the subsidiaries to participate in the energy-optimized strategy. Then, a novel hybrid MONSGA-II&MSNE approach is presented to address the integrated problem. To effectively optimize the two strategies, the MONSGA-II is improved by the multi-oriented optimization heuristic strategy in two aspects: 1) enhancing the local search ability of NSGA-II and 2) solving the matching conflict problem in the crossover operation. The mixed strategy Nash equilibrium (MSNE) is applied to calculate the cost-optimal reward mechanism under different game combinations. Finally, the performance of the proposed approach is demonstrated in the case study.

A novel energy-efficient clustering algorithm was proposed which aimed at improving the energy efficiency of WSNs via reducing and balancing energy consumption in this paper. The lemma concerning the dual-cluster-head mechanism which was designed to reduce the energy overhead during the process of rotation of Cluster Heads (CHs) was proposed and proven at first. In addition, a non-cooperative game model was presented with the purpose of balancing the energy consumption among the Cluster Heads. Besides, the Nash Equilibrium Point (NEP) of the game model was presented and the corresponding proof was provided. Subsequently, the Energy-efficient Clustering algorithm combined Game theory and Dual-cluster-head (ECGD) mechanism was detailed, which took the energy efficiency in both of the intra-cluster and inter-cluster communication into consideration. Finally, extensive experiments were conducted via simulation and the simulation results were compared with the existing Clustering strategies in terms of energy efficiency and network performance. The analyses of results have shown that the ECGD can improve energy efficiency and extend the network lifespan effectively.

In device-to-device (D2D) communications underlaying cellular systems based on the cloud radio access network, including distributed remote radio heads (RRHs) and centralized BaseBand Unit (BBU) pool, due to dense deployment and spectrum reuse, there are strong intra-cell interference and inter-cell interference, which will severely degrade both the energy efficiency (EE) and the quality of service. To address this problem, we propose an energy-efficient resource allocation scheme to determine channel selection and power allocation by introducing the relay-aided in-band D2D communication mode and the non-cooperative game theory. We explore the above resource allocation problem in a hybrid manner and model it as a non-cooperative game, where each player optimizes its EE individually with the aid of RRHs. Then, we alleviate the inter-cell interference from the cellular UEs near the cell edge by allowing these UEs to select in-band D2D relay links to shorten the long transmission distances between them and RRHs. Moreover, the interfering signal processing load of the BBU is lowered due to the reduction of the interfering signal strength, and the EE is improved due to the reduction of transmission powers of these cellular UEs. The achievable performance of the proposed scheme is analyzed through simulations.

A solution to help victims against phishing is anticipating and leveraging impacts related to phisher actions.In this regard, this work reshapes game theoretical logic between Intrusion Detection System (IDS) agents andinsiders to email spear-phishing interactions. The email spear-phishing attack is designed as a non-cooperativeand repeated game between opponents. Additionally, this work relies on Quantal Response Equilibrium (QRE)to build a game theoretical approach to predict the phisher’s future intent based on past actions of bothplayers. This approach is coupled with a recommendation strategy of appropriate allocation of resources toinvest to strengthen user protection. Simulations on spear-phishing scenarios demonstrate the ability of thefinal system to intuitively guess the most likely phisher decisions. This work provides intelligence to spear-phishing detectors and humans such that they can anticipate next phisher actions.

The aim of the paper is to compare the sensitivity of a government’s fiscal policy and a central bank’s monetary policy, which are in Nash equilibrium in the case of a non-cooperative game between the government and the central bank in Czechia, Hungary, and Romania. The analysis for each country is conducted from the date of its accession to the European Union. The research period for Czechia and Hungary includes the quarters 2004Q2-2019Q2, and for Romania, 2007Q1-2019Q2. The study has demonstrated that in Romania the government’s response to interest rate changes is the strongest and the central bank’s response to changes in the budget deficit turned out to be the weakest. On the other hand, the strongest response of the central bank to changes in the budget deficit turned out to be in Hungary, which means that the central bank in Hungary makes a significant correction of interest rates as a result of changes in the budget deficit.

Under the “double carbon” goal and background, new energy power generation will usher in great development. The investment and construction of new energy projects and the scale of grid connected transmission are increasing, which puts forward higher requirements for the investment decision-making management and income of county new energy subjects. Based on the power curve trading and non cooperative game theory and the day ahead real-time two-stage adjustment and correction mechanism of county subjects, this paper briefly analyzes the new energy consumption and income of county subjects based on internal non cooperative game under curve trading.

This paper introduced Helbing’s social force model, modified it with game theory. Then how individuals in the space behave in dynamic non-cooperative games was described, different macro grouping characteristics were obtained. Individual behaviours at the micro level were simulated. Setting different parameters and conditions of the model, the macro effects of individual behaviours were observed. The overall behaviour of the system was studied. It could be used to guide the allocation of public resources.

The paper introduces the positional cooperative and non-cooperative game of a greater number of met ships for the description of the process considered as well as for the synthesis of optimal control strategies of the own ship in collision situation. The approximated mathematical model of differential game in the form of triple linear programming problem is used for the synthesis of safe ship trajectory as a multistage process decision. The considerations have been illustrated an example of program computer simulation to determine the safe ship trajectories in situation of passing a many of the ships encountered.

Abstract With the development of smart grids, a renewable energy generation system has been introduced into a smart house. The generation system usually supplies a storage system with the capability to store the produced energy for satisfying a user’s future demand. In this paper, the main objective is to determine the best strategies of energy consumption and optimal storage capacities for residential users, which are both closely related to the energy cost of the users. Energy management with storage capacity optimization is studied by considering the cost of renewable energy generation, depreciation cost of storage and bidirectional energy trading. To minimize the cost to residential users, the non-cooperative game-theoretic method is employed to formulate the model that combines energy consumption and storage capacity optimization. The distributed algorithm is presented to understand the Nash equilibrium which can guarantee Pareto optimality in terms of minimizing the energy cost. Simulation results show that the proposed game approach can significantly benefit residential users. Furthermore, it also contributes to reducing the peak-to-average ratio (PAR) of overall energy demand.

This paper suggests that the efficiency of a system (decision-making unit) and its subsystem cannot be properly measured using a two-stage data envelopment analysis (DEA) model either in cooperative or non-cooperative evaluation. Indeed, the existing methods subjectively determine the status of the subsystems in the whole system. The two-stage DEA models, either cooperative game or non-cooperative game, are used to analyze the environmental efficiency. However, when the actual relationship between the two subsystems is inconsistent with the subjective relationship assumptions, the overall efficiency of the system and the efficiency of each subsystem will be biased. The conventional two-stage DEA models require predetermining the relationship between the subsystems within the system based on the subjective judgment of the decision-maker. Based on this, this paper proposes a three-step method to solve the two-stage DEA. First, the position relation among subsystems is determined according to the optimal weights through the model. According to the status relationship among subsystems, the decision units are grouped, and the two-stage DEA model of cooperative game or non-cooperative game is used to analyze the efficiency in each group. This method reduces the subjectivity of decision making and analyzes the efficiency of each decision unit applying the most appropriate two-stage DEA model to find the source of inefficiency. Finally, this paper verifies the rationality and validity of the method by analyzing the water use efficiency of industrial systems in China. It is found that most regions in China value economic development more than environmental protection (as evidenced by the DEA weights). What is more, the method proposed by the paper can be generalized for any two-stage DEA problem.

The energy-efficient resource allocation problem was taken in an ultra-dense network(UDN) consisted of multiple femtocells.Aiming at maximizing the energy efficiency (EE) of the whole network,quality of service (QoS) constraint and interference limitation was considered.Then,the established nonconvex and nonlinear problem was relaxed relying on Cauchy inequality,and was developed into a non-cooperative game.Additionally,a distributed EE maximization algorithm was proposed satisfying the max-min fairness (MMF) criterion.Simulation results show that the proposed algorithm outperformances the existing algorithms in terms of the EE and the throughput.

In vehicular ad hoc networks (VANETs), vehicles broadcast their status information in beacons periodically to make the surrounding vehicles aware of their presence. To maximize the level of awareness, a congestion control mechanism is necessary to avoid loss of beacons due to collision in dense traffic environments. In addition to congestion control, it is desirable that vehicles share network bandwidth in a manner proportional to their dynamics or safety application requirements. Current congestion control mechanisms have a number of issues including control information overheads, fairness, and awareness. In this paper, a beacon rate and awareness control mechanism based on non-cooperative game theory called non-cooperative beacon rate and awareness control (NORAC), is proposed. The existence and uniqueness of the Nash equilibrium of the game is proved mathematically and an algorithm is proposed to find the equilibrium point in a distributed manner. The proposed algorithm is used to assign a beacon rate to every vehicle proportional to its requirements, while ensuring fairness between vehicles with the same requirement. NORAC is compared with the two other known congestion control mechanisms. The simulation results show the efficiency and stability of the proposed NORAC algorithm in several high-density traffic scenarios. The results indicate its advantages in terms of fairness and congestion and awareness control over the other two algorithms, while not requiring excessive information to be included in beacons.

A problem of evaluating the non-cooperative game model is considered in the paper. The evaluation is understood in the sense of obtaining the game payoff matrices whose entries are single-point values. Experts participating in the estimation procedure make their judgments on all the game situations for every player. A form of expert estimations is suggested. The form is of binary type, wherein the expert’s judgment is either 1 or 0. This type is the easiest to be implemented in social networks. For most social networks, 1 can be a “like” (the currently evaluated situation is advantageous), and 0 is a “dislike” (disadvantageous). A method of processing expert estimations is substantiated. Two requirements are provided for obtaining disambiguous payoff averages along with the clustered payoff matrices.

We consider pseudo-simultaneous normal form games - strategic games with rules violated by information leaks and simultaneity corruption. We provide classification and construction of a game taxonomy based on applicable solution principles. Existence conditions are highlighted, formulated and analysed.

In a deregulated environment of the power market, in order to lower their energy price and guarantee the stability of the power network, appropriate transmission lines have to be considered for electricity generators to sell their energy to the end users. This paper proposes a game-theoretic power transmission scheduling for multiple generators to lower their wheeling cost. Based on the embedded cost method, a wheeling cost model consisting of congestion cost, cost of losses and cost of transmission capacity is presented. By assuming each generator behaves in a selfish and rational way, the competition among the multiple generators is formulated as a non-cooperative game, where the players are the generators and the strategies are their daily schedules of power transmission. We will prove that there exists at least one pure-strategy Nash equilibrium of the formulated power transmission game. Moreover, a distributed algorithm will be provided to realize the optimization in terms of minimizing the wheeling cost. Finally, simulations were performed and discussed to verify the feasibility and effectiveness of the proposed non-cooperative game approach for the generators in a deregulated environment.

With the reform of electricity markets, demand response (DR) plays an important role in providing flexibility to the markets. Block bidding market is a new market mode, which is based on the concept of “the same quality, the same price”. The mechanism has great effects in reducing start-stop related costs. In this paper, we propose a double-sided non-cooperative game model in block bidding markets with a DR program. The model combines the advantages of block bidding and the simplicity of hourly bidding. In the model, one side is the non-cooperative game of supply-side power firms, and we propose a novel supply function bidding model based on block duration and load capacity to maximize each firm’s profit. The other side is the demand-side different types of customers, and we propose a DR model that combines hourly-various prices with the block bidding mechanism to maximize each customer’s payoff. The overall market optimization problem is solved by a distributed iterative algorithm, which has great convergence performance. We verify the proposed model on real data, and the results show that the demand load curve becomes flattened with DR, and the total generation costs decrease while the social welfare is significantly improved.

This work focuses on the demand response (DR) participation using the energy storage system (ESS). A probabilistic Gaussian mixture model based on market operating results Monte, Carlo Simulation (MCS), is required to respond to an urgent DR signal. However, there is considerable uncertainty in DR forecasting, which occasionally fails to predict DR events. Because this failure is attributable to the intermittency of the DR signals, a non-cooperative game model that is useful for decision-making on DR participation is proposed. The game is conducted with each player holding a surplus of energy but incomplete information. Consequently, each player can share unused electricity during DR events, engaging in indirect energy trading (IET) under a non-cooperative game framework. The results of the game, the Nash equilibrium (N.E.), are verified using a case study with relevant analytical data from the campus of Gwangju Institute of Science and Technology (GIST) in Korea. The results of the case study show that IET is useful in mitigating the uncertainty of the DR program.

Power control is one of the key technologies of cognitive radio technology. Distributed power control problem can be converted into non-cooperative game to solve the problem. Combining with the characteristics of cognitive radio, a new type S utility function was put forwarded, the normalized form was applied, and the existence and uniqueness of the Nash equilibrium were proved. Simulation results show that the algorithm is not restricted by system modulation mode, and reduces the computational complexity, and has faster convergence speed. The fairness between the users was taken into account, to a certain extent, and the users can share channel resources fairly.

Access control technology is an important information security technology to protect the sensitive information and critical resources in computer system and network.But traditional access control methods could only respond to access requests of users passively and can’t meet the changing dynamic network environment.In order to improve the ability to respond to malicious attacks and threats in access control system,a security mechanism is designed,which is suitable for access control,based on non-cooperative game theory in the game.When the subject makes an access request to the object,there will be a non-cooperative game between them to get Nash equilibrium.Then the security mechanism will compare the probabilities in the Nash equilibrium to the setting thresholds to get the conclusion that whether to authorize the subject or not.Experiment proves the effectiveness of the security mechanisms.