Design and pricing of maintenance service contract based on Nash non-cooperative game approach

Nowadays manufacturers are facing fierce challenge.Apart from the products,providing customers with multiple maintenance options in the service contract becomes more popular,since it can help to improve customer satisfaction,and ultimately promote sales and maximize profit for the manufacturer.By considering the combinations of corrective maintenance and preventive maintenance,totally three types of maintenance service contracts are designed.Moreover,attractive incentive and penalty mechanisms are adopted in the contracts.On this basis,Nash non-cooperative game is applied to analyze the revenue for both the manufacturer and customers,and so as to optimize the pricing mechanism of maintenance service contract and achieve a win-win situation.Numerical experiments are conducted.The results show that by taking into account the incentive and penalty mechanisms,the revenue can be improved for both the customers and manufacturer.Moreover,with the increase of repair rate and improvement factor in the preventive maintenance,the revenue will increase gradually for both the parties.

Non-Cooperative Game of Coordinated Scheduling of Parallel Machine Production and Transportation in Shared Manufacturing

Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry,the coordinated scheduling problem of parallel machine production and transportation is investigated.The problem takes into account the coordination of production and transportation before production as well as the disparities in machine spatial position and performance.A non-cooperative game model is established,considering the competition and self-interest behavior of jobs from different customers for machine resources.The job from different customers is mapped to the players in the game model,the corresponding optional processing machine and location are mapped to the strategy set,and the makespan of the job is mapped to the payoff.Then the solution of the scheduling model is transformed into the Nash equilibrium of the non-cooperative game model.A Nash equilibrium solution algorithm based on the genetic algorithm(NEGA)is designed,and the effective solution of approximate Nash equilibrium for the game model is realized.The fitness function,single-point crossover operator,and mutation operator are derived from the non-cooperative game model’s characteristics and the definition of Nash equilibrium.Rules are also designed to avoid the generation of invalid offspring chromosomes.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.Compared with other algorithms such as heuristic algorithms(FCFS,SPT,and LPT),the simulated annealing algorithm(SA),and the particle swarm optimization algorithm(PSO),experimental results show that the proposed NE-GA algorithm has obvious performance advantages.

Peer-to-Peer Energy Trading Method of Multi-Virtual Power Plants Based on Non-Cooperative Game

The current electricity market fails to consider the energy consumption characteristics of transaction subjects such as virtual power plants.Besides,the game relationship between transaction subjects needs to be further explored.This paper proposes a Peer-to-Peer energy trading method for multi-virtual power plants based on a non-cooperative game.Firstly,a coordinated control model of public buildings is incorporated into the scheduling framework of the virtual power plant,considering the energy consumption characteristics of users.Secondly,the utility functions of multiple virtual power plants are analyzed,and a non-cooperative game model is established to explore the game relationship between electricity sellers in the Peer-to-Peer transaction process.Finally,the influence of user energy consumption characteristics on the virtual power plant operation and the Peer-to-Peer transaction process is analyzed by case studies.Furthermore,the effect of different parameters on the Nash equilibrium point is explored,and the influence factors of Peer-to-Peer transactions between virtual power plants are summarized.According to the obtained results,compared with the central air conditioning set as constant temperature control strategy,the flexible control strategy proposed in this paper improves the market power of each VPP and the overall revenue of the VPPs.In addition,the upper limit of the service quotation of the market operator have a great impact on the transaction mode of VPPs.When the service quotation decreases gradually,the P2P transaction between VPPs is more likely to occur.

Coordinated Scheduling of Two-Agent Production and Transportation Based on Non-Cooperative Game

A two-agent production and transportation coordinated scheduling problem in a single-machine environment is suggested to compete for one machine from different downstream production links or various consumers.The jobs of two agents compete for the processing position on a machine,and after the pro-cessed,they compete for the transport position on a transport vehicle to be trans-ported to two agents.The two agents have different objective functions.The objective function of the first agent is the sum of the makespan and the total trans-portation time,whereas the objective function of the second agent is the sum of the total completion time and the total transportation time.Given the competition between two agents for machine resources and transportation resources,a non-cooperative game model with agents as game players is established.The job pro-cessing position and transportation position corresponding to the two agents are mapped as strategies,and the corresponding objective function is the utility func-tion.To solve the game model,an approximate Nash equilibrium solution algo-rithm based on an improved genetic algorithm(NE-IGA)is proposed.The genetic operation based on processing sequence and transportation sequence,as well as the fitness function based on Nash equilibrium definition,are designed based on the features of the two-agent production and transportation coordination scheduling problem.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.When compared to heuristic rules such as the Longest Processing Time first(LPT)and the Shortest Processing Time first(SPT),the objective function values of the two agents are reduced by 4.3%and 2.6% on average.

Sequential quadratic programming-based non-cooperative target distributed hybrid processing optimization method

The distributed hybrid processing optimization problem of non-cooperative targets is an important research direction for future networked air-defense and anti-missile firepower systems. In this paper, the air-defense anti-missile targets defense problem is abstracted as a nonconvex constrained combinatorial optimization problem with the optimization objective of maximizing the degree of contribution of the processing scheme to non-cooperative targets, and the constraints mainly consider geographical conditions and anti-missile equipment resources. The grid discretization concept is used to partition the defense area into network nodes, and the overall defense strategy scheme is described as a nonlinear programming problem to solve the minimum defense cost within the maximum defense capability of the defense system network. In the solution of the minimum defense cost problem, the processing scheme, equipment coverage capability, constraints and node cost requirements are characterized, then a nonlinear mathematical model of the non-cooperative target distributed hybrid processing optimization problem is established, and a local optimal solution based on the sequential quadratic programming algorithm is constructed, and the optimal firepower processing scheme is given by using the sequential quadratic programming method containing non-convex quadratic equations and inequality constraints. Finally, the effectiveness of the proposed method is verified by simulation examples.

Non-Cooperative Differential Game Based Energy Consumption Control for Dynamic Demand Response in Smart Grid

In this paper, we conduct research on the dynamic demand response problem in smart grid to control the energy consumption. The objective of the energy consumption control is constructed based on differential game, as the dynamic of each users’ energy state in smart gird can be described based on a differential equation. Concept of electricity sharing is introduced to achieve load shift of main users from the high price hours to the low price hours. Nash equilibrium is given based on the Hamilton equation and the effectiveness of the proposed model is verified based on the numerical simulation results.

Resource Allocation for Network Security Risk Assessment：A Non-Cooperative Differential Game Based Approach

In this paper, we propose a non-cooperative differential game theory based resource allocation approach for the network security risk assessment. For the risk assessment, the resource will be used for risk assess, including response cost and response negative cost. The whole assessment process is considered as a differential game for optimal resource control. The proposed scheme can be obtained through the Nash Equilibrium. It is proved that the game theory based algorithm is applicable and the optimal resource level can be achieved based on the proposed algorithm.

A Non-Cooperative Differential Game-Based Security Model in Fog Computing

Fog computing is a new paradigm providing network services such as computing, storage between the end users and cloud. The distributed and open structure are the characteristics of fog computing, which make it vulnerable and very weak to security threats. In this article, the interaction between vulnerable nodes and malicious nodes in the fog computing is investigated as a non-cooperative differential game. The complex decision making process is reviewed and analyzed. To solve the game, a fictitious play-based algorithm is which the vulnerable node and the malicious nodes reach a feedback Nash equilibrium. We attain optimal strategy of energy consumption with Qo S guarantee for the system, which are conveniently operated and suitable for fog nodes. The system simulation identifies the propagation of malicious nodes. We also determine the effects of various parameters on the optimal strategy. The simulation results support a theoretical foundation to limit malicious nodes in fog computing, which can help fog service providers make the optimal dynamic strategies when different types of nodes dynamically change their strategies.

Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game

The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.

A game-theoretic approach for federated learning:A trade-off among privacy,accuracy and energy

Benefiting from the development of Federated Learning(FL)and distributed communication systems,large-scale intelligent applications become possible.Distributed devices not only provide adequate training data,but also cause privacy leakage and energy consumption.How to optimize the energy consumption in distributed communication systems,while ensuring the privacy of users and model accuracy,has become an urgent challenge.In this paper,we define the FL as a 3-layer architecture including users,agents and server.In order to find a balance among model training accuracy,privacy-preserving effect,and energy consumption,we design the training process of FL as game models.We use an extensive game tree to analyze the key elements that influence the players’decisions in the single game,and then find the incentive mechanism that meet the social norms through the repeated game.The experimental results show that the Nash equilibrium we obtained satisfies the laws of reality,and the proposed incentive mechanism can also promote users to submit high-quality data in FL.Following the multiple rounds of play,the incentive mechanism can help all players find the optimal strategies for energy,privacy,and accuracy of FL in distributed communication systems.

Non-Cooperative Behavior Management in Large-Scale Group Decision-Making Considering the Altruistic Behaviors of Experts and Its Application in Emergency Alternative Selection

Emergency decision-making problems usually involve many experts with different professional backgrounds and concerns,leading to non-cooperative behaviors during the consensus-reaching process.Many studies on noncooperative behavior management assumed that the maximumdegree of cooperation of experts is to totally accept the revisions suggested by the moderator,which restricted individuals with altruistic behaviors to make more contributions in the agreement-reaching process.In addition,when grouping a large group into subgroups by clustering methods,existing studies were based on the similarity of evaluation values or trust relationships among experts separately but did not consider them simultaneously.In this study,we introduce a clustering method considering the similarity of evaluation values and the trust relations of experts and then develop a consensusmodel taking into account the altruistic behaviors of experts.First,we cluster experts into subgroups by a constrained Kmeans clustering algorithm according to the opinion similarity and trust relationship of experts.Then,we calculate the weights of experts and clusters based on the centrality degrees of experts.Next,to enhance the quality of consensus reaching,we identify three kinds of non-cooperative behaviors and propose corresponding feedback mechanisms relying on the altruistic behaviors of experts.A numerical example is given to show the effectiveness and practicality of the proposed method in emergency decision-making.The study finds that integrating altruistic behavior analysis in group decision-making can safeguard the interests of experts and ensure the integrity of decision-making information.

Power Control Algorithm of Cognitive Radio Based on Non-Cooperative Game Theory

This paper addresses the power con- trol problems of Cognitive Radio （CR） trader transmission power and interference tempera- ture constraints. First, we propose the interfer- ence constraint which ensures that the Quality of Service （QoS） standards for primary users is considered and a non-cooperative game power control model. Based on the proposed model, we developed a logical utility function based on the Signal-to-Interference-Noise Ratio （S/NR） and a novel algorithm network power control. that is suitable for CR Then, the existence and uniqueness of the Nash Equilibrium （NE） in our utility function are proved by the principle of game theory and the corresponding optimi- zations. Compared to traditional algorithms, the proposed one could converge to an NE in 3-5 iterative operations by setting an appropriate pricing factor. Finally, simulation results ver- ified the stability and superiority of the novel algorithm in flat-fading channel environments.

QoS awared power and admission controls based on non-cooperative game theory in wireless networks

In order to better accommodate heterogeneous quality of service (QoS) in wireless networks, an algorithm called QoS-aware power and admission controls (QAPAC) is proposed. The system is modeled as a non-cooperative game where the users adjust their transmit powers to maximize the utility, thus restraining the interferences. By using adaptive utility functions and tunable pricing parameters according to QoS levels, this algorithm can well meet different QoS requirements and improve system capacity compared with those that ignore the QoS differences.

An Optimized Resource Scheduling Strategy for Hadoop Speculative Execution Based on Non-cooperative Game Schemes

Hadoop is a well-known parallel computing system for distributed computing and large-scale data processes.“Straggling”tasks,however,have a serious impact on task allocation and scheduling in a Hadoop system.Speculative Execution(SE)is an efficient method of processing“Straggling”Tasks by monitoring real-time running status of tasks and then selectively backing up“Stragglers”in another node to increase the chance to complete the entire mission early.Present speculative execution strategies meet challenges on misjudgement of“Straggling”tasks and improper selection of backup nodes,which leads to inefficient implementation of speculative executive processes.This paper has proposed an Optimized Resource Scheduling strategy for Speculative Execution(ORSE)by introducing non-cooperative game schemes.The ORSE transforms the resource scheduling of backup tasks into a multi-party non-cooperative game problem,where the tasks are regarded as game participants,whilst total task execution time of the entire cluster as the utility function.In that case,the most benefit strategy can be implemented in each computing node when the game reaches a Nash equilibrium point,i.e.,the final resource scheduling scheme to be obtained.The strategy has been implemented in Hadoop-2.x.Experimental results depict that the ORSE can maintain the efficiency of speculative executive processes and improve fault-tolerant and computation performance under the circumstances of Normal Load,Busy Load and Busy Load with Skewed Data.

Non-cooperative game for network access selection in heterogeneous integrated networks

The integration of different heterogeneous access networks is one of the remarkable characteristics of the next generation network,in which users with multi-network interface terminals can independently select access network to obtain the most desired service.A kind of unified quantification model of non-monotone quality of service(QoS) and a model of non-cooperative game between users and networks are proposed for heterogeneous network access selection.An optimal network pricing mechanism could be formulated by using a novel strategy which is used in this non-cooperative game model to balance the interests of both the users and the networks.This access network selection mechanism could select the most suitable network for users,and it also could provide the basis when formulating QoS standards in heterogeneous integrated networks.The simulation results show that this network selection decision-making algorithm can meet the users' demand for different levels service in different scenes and it can also avoid network congestion caused by unbalanced load.

Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space

The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.

Ready,set,go:Medical preparations for the Paris 2024 Paralympic Games

1.Introduction In August 2024,over 4400 Paralympic athletes will gather in Paris for the Paralympic Summer Games—the pinnacle of every Paralympian’s(Para athletes competing at the Paralympic Games)career to showcase their ability and skills.Their training,preparation,and effort in the years leading up to the Games are unparalleled.To achieve success,Paralympians specifically rely on a medical support team to achieve their goals.So,what is required of the medical support team to prepare Paralympians to get ready,set,and go to Paris 2024?

Effect of distribution of fines on evolution of cooperation in spatial public goods game

In the realm of public goods game,punishment,as a potent tool,stands out for fostering cooperation.While it effectively addresses the first-order free-rider problem,the associated costs can be substantial.Punishers incur expenses in imposing sanctions,while defectors face fines.Unfortunately,these monetary elements seemingly vanish into thin air,representing a loss to the system itself.However,by virtue of the redistribution of fines to cooperators and punishers,not only can we mitigate this loss,but the rewards for these cooperative individuals can be enhanced.Based upon this premise,this paper introduces a fine distribution mechanism to the traditional pool punishment model.Under identical parameter settings,by conducting a comparative experiment with the conventional punishment model,the paper aims to investigate the impact of fine distribution on the evolution of cooperation in spatial public goods game.The experimental results clearly demonstrate that,in instances where the punishment cost is prohibitively high,the cooperative strategies of the traditional pool punishment model may completely collapse.However,the model enriched with fine distribution manages to sustain a considerable number of cooperative strategies,thus highlighting its effectiveness in promoting and preserving cooperation,even in the face of substantial punishment cost.

Problematic Use of Video Games in Schools in Northern Benin (2023)

Objective: To study the problematic use of video games among secondary school students in the city of Parakou in 2023. Methods: Descriptive cross-sectional study conducted in the commune of Parakou from December 2022 to July 2023. The study population consisted of students regularly enrolled in public and private secondary schools in the city of Parakou for the 2022-2023 academic year. A two-stage non-proportional stratified sampling technique combined with simple random sampling was adopted. The Problem Video Game Playing (PVP) scale was used to assess problem gambling in the study population, while anxiety and depression were assessed using the Hospital Anxiety and Depression Scale (HADS). Results: A total of 1030 students were included. The mean age of the pupils surveyed was 15.06 ± 2.68 years, with extremes of 10 and 28 years. The [13 - 18] age group was the most represented, with a proportion of 59.6% (614) in the general population. Females predominated, at 52.8% (544), with a sex ratio of 0.89. The prevalence of problematic video game use was 24.9%, measured using the Video Game Playing scale. Associated factors were male gender (p = 0.005), pocket money under 10,000 cfa (p = 0.001) and between 20,000 - 90,000 cfa (p = 0.030), addictive family behavior (p < 0.001), monogamous family (p = 0.023), good relationship with father (p = 0.020), organization of video game competitions (p = 0.001) and definite anxiety (p Conclusion: Substance-free addiction is struggling to attract the attention it deserves, as it did in its infancy everywhere else. This study complements existing data and serves as a reminder of the need to focus on this group of addictions, whose problematic use of video games remains the most frequent due to its accessibility and social tolerance. Preventive action combined with curative measures remains the most effective means of combating the problem at national level.

Evolutionary dynamics of tax-based strong altruistic reward andpunishment in a public goods game

In public goods games, punishments and rewards have been shown to be effective mechanisms for maintaining individualcooperation. However, punishments and rewards are costly to incentivize cooperation. Therefore, the generation ofcostly penalties and rewards has been a complex problem in promoting the development of cooperation. In real society,specialized institutions exist to punish evil people or reward good people by collecting taxes. We propose a strong altruisticpunishment or reward strategy in the public goods game through this phenomenon. Through theoretical analysis and numericalcalculation, we can get that tax-based strong altruistic punishment (reward) has more evolutionary advantages thantraditional strong altruistic punishment (reward) in maintaining cooperation and tax-based strong altruistic reward leads toa higher level of cooperation than tax-based strong altruistic punishment.