A Value for Games Defined on Graphs

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

Cooperative game theory-based steering law design of a CMG system

Spacecraft require a large-angle manoeuvre when performing agile manoeuvring tasks, therefore a control moment gyroscope(CMG) is employed to provide a strong moment.However, the control of the CMG system easily falls into singularity, which renders the actuator unable to output the required moment. To solve the singularity problem of CMGs, the control law design of a CMG system based on a cooperative game is proposed. First, the cooperative game model is constructed according to the quadratic programming problem, and the cooperative strategy is constructed. When the strategy falls into singularity, the weighting coefficient is introduced to carry out the strategy game to achieve the optimal strategy. In theory, it is proven that the cooperative game manipulation law of the CMG system converges, the sum of the CMG frame angular velocities is minimized, the energy consumption is small, and there is no output torque error. Then, the CMG group system is simulated.When the CMG system is near the singular point, it can quickly escape the singularity. When the CMG system falls into the singularity, it can also escape the singularity. Considering the optimization of angular momentum and energy consumption, the feasibility of the CMG system steering law based on a cooperative game is proven.

A cooperative detection game:UAV swarm vs.one fast intruder

This paper studies a special defense game using unmanned aerial vehicle(UAV)swarm against a fast intruder.The fast intruder applies an offensive strategy based on the artificial potential field method and Apollonius circle to scout a certain destination.As defenders,the UAVs are arranged into three layers:the forward layer,the midfield layer and the back layer.The co-defense mechanism,including the role derivation method of UAV swarm and a guidance law based on the co-defense front point,is introduced for UAV swarm to co-detect the intruder.Besides,five formations are designed for comparative analysis when ten UAVs are applied.Through Monte Carlo experiments and ablation experiment,the effectiveness of the proposed co-defense method has been verified.

Cooperative and Competitive Multi-Agent Systems:From Optimization to Games

Multi-agent systems can solve scientific issues related to complex systems that are difficult or impossible for a single agent to solve through mutual collaboration and cooperation optimization.In a multi-agent system,agents with a certain degree of autonomy generate complex interactions due to the correlation and coordination,which is manifested as cooperative/competitive behavior.This survey focuses on multi-agent cooperative optimization and cooperative/non-cooperative games.Starting from cooperative optimization,the studies on distributed optimization and federated optimization are summarized.The survey mainly focuses on distributed online optimization and its application in privacy protection,and overviews federated optimization from the perspective of privacy protection me-chanisms.Then,cooperative games and non-cooperative games are introduced to expand the cooperative optimization problems from two aspects of minimizing global costs and minimizing individual costs,respectively.Multi-agent cooperative and non-cooperative behaviors are modeled by games from both static and dynamic aspects,according to whether each player can make decisions based on the information of other players.Finally,future directions for cooperative optimization,cooperative/non-cooperative games,and their applications are discussed.

Diffusion mechanism simulation of cloud manufacturing complex network based on cooperative game theory

Cloud manufacturing is a specific implementation form of the "Internet + manufacturing" strategy. Why and how to develop cloud manufacturing platform(CMP), however, remains the key concern of both platform operators and users. A microscopic model is proposed to investigate advantages and diffusion forces of CMP through exploration of its diffusion process and mechanism. Specifically, a three-stage basic evolution process of CMP is innovatively proposed. Then, based on this basic process, a more complex CMP evolution model has been established in virtue of complex network theory, with five diffusion forces identified. Thereafter, simulations on CMP diffusion have been conducted. The results indicate that, CMP possesses better resource utilization,user satisfaction, and enterprise utility. Results of simulation on impacts of different diffusion forces show that both the time required for CMP to reach an equilibrium state and the final network size are affected simultaneously by the five diffusion forces. All these analyses indicate that CMP could create an open online cooperation environment and turns out to be an effective implementation of the "Internet + manufacturing" strategy.

Profit Allocation Scheme Among Players in Supply-Chain Based on Shapley Value of Fuzzy Bi-cooperative Games

The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.

Game theory approach to optimal capital cost allocation in pollution control

This paper tries to integrate game theory, a very useful tool to resolve conflict phenomena, with optimal capital cost allocation issue in total emission control. First the necessity of allocating optimal capital costs fairly and reasonably among polluters in total emission control was analyzed. Then the possibility of applying game theory to the issue of the optimal capital cost allocation was expounded. Next the cooperative N person game model of the optimal capital cost allocation and its solution ways including method based on Shapley value, least core method, weak least core methods, proportional least core method, CGA method, MCRS method and so on were delineated. Finally through application of these methods it was concluded that to apply game theory in the optimal capital cost allocation issue is helpful to implement the total emission control planning schemes successfully, to control pollution effectively, and to ensure sustainable development.

A NOVEL COOPERATIVE SPECTRUM SENSING METHOD BASED ON COOPERATIVE GAME THEORY

A novel cooperative sensing method is proposed in this paper. The proposed scheme adopts sensing creditability degree to characterize the impact of the distance and the channel parameters on the sensing result,and considers that each user has different average SNR and different decision threshold,by using General Nash Bargaining Solution (GNBS) strategy in Cooperative Game Theory (CGT),the detection performance for two-user case are derived. For multi-user case,the sensing performance is obtained with Hungarian method. Compared with the traditional schemes such as Nash Bargaining Solution (NBS) and AND,the proposed scheme covers all the factors mentioned above,and enhances the sensing rationality and reliability. Simulation results show that the proposed scheme can further improve the sensing performance and creditability.

Shapley Value for Cooperative Games with Fuzzy Coalition

Fuzzy Shapley values are developed based on conventional Shapley value. This kind of fuzzy cooperative games admit the representation of rates of players＇ participation to each coalition. And they can be applicable to both supperadditive and subadditvie cooperative games while other kinds of fuzzy cooperative games can only be superadditive. An explicit form of the Shapley function on fuzzy games with λ-fuzzy measure was also proposed.

Bargaining Game Theoretic Power Control in Selfish Cooperative Relay Networks

Wireless cooperative communications require appropriate power allocation （PA） between the source and relay nodes. In selfish cooperative communication networks, two partner user nodes could help relaying information for each other, but each user node has the incentive to consume his power solely to decrease its own symbol error rate （SER） at the receiver. In this paper, we propose a fair and efficient PA scheme for the decode-and-forward cooperation protocol in selfish cooperative relay networks. We formulate this PA problem as a two-user cooperative bargaining game, and use Nash bargaining solution （NBS） to achieve a win-win strategy for both partner users. Simulation results indicate that the NBS is fair in that the degree of cooperation of a user only depends on how much contribution its partner can make to decrease its SER at the receiver, and efficient in the sense that the SER performance of both users could be improved through the game.

The Coalition Cooperative Game Method and Its Application in Multi-objective Optimization Design

This paper proposes a multi-objective optimization design method based on the coalition cooperative game theory where the three design goals have been seen as three game players. By calculating the affecting factors and fuzzy clustering, the design variables are divided into different strategic spaces which belong to each player, then it constructs a payoff function based on the coalition mechanism. Each game player takes its own revenue function as a target and obtains the best strategy versus other players. The best strategies of all players consist of the strategy permutation of a round game and it obtains the final game solutions through multi-round games according to the convergence criterion. A multi-objective optimization example of the luff mechanism of compensative sheave block shows the effectiveness of the coalition cooperative game method.

Equilibrium solution of two enterprises cooperative game

Based on the actual experience of cooperation in the supply chain, the Nash solution of two enterprises cooperative games is given. Not only is the solution unique, but it is also stable, and neither side has the capability to deviate the allocation of interests from the equilibrium point. If some firm tries to withdraw from cooperation or threaten to use other particular strategy, the negotiations are likely to achieve the distribution by the threat game; The calculating method of the choice of the optimal bargaining base point and the corresponding optimal pay-off vector are given.

ON THE NON－COMPACTNESS OF THE CORE OF NONATOMIC CONVEX σ－CONTINUOUS MEASURE GAMES

This paper concerns with the core of nonatomic games of form f(μ), where μ is a nonatomic nonnegative measure and f is a continuous convex function on the domain of μ. The main result of this paper is that the core of the game is not compact under the norm topology unless the game itself is a measure. This shows the largeness of the core in a sense other than that defined by Sharky for finite cases.

On Aspiration Solutions in Predicting Coalition Formationin Cooperative Games

This paper consists of two parts. The first part introduces the strict aspiration as a new aspiration solution concept, which is provedto be existent for any cooperative game. The second part deals with theunsolved problem put forward by Bennett by showing that there is atleast one payoff which is balanced, partnered and equal gains aspiration.The proof is algebraic and constructive, thus providing an algorithm forfinding such aspirations.

Invasive Species Control Based on a Cooperative Game

We develop a long-term dynamic model for controlling invasive species using the theory of cooperative games. The model is applied to control of invasive buffelgrass in the Arizona desert, which directly competes with indigenous species and can increase wildfire risk. Interest groups care about damages to three threatened resources: saguaro, cactus, riparian vegetation, and buildings. The model optimally allocates labor and a budget to protect these resources by controlling the buffelgrass population over a multi-period planning horizon. The solution is based on computing the Shapley values for the interest groups. A homeowner strategy of creating defensible space around structures to protect against wildfire affords less protection to the other resources. A similar result holds for protection of saguaros, which are also spatially concentrated. Under the optimal solution, groups caring about spatially-dispersed, riparian vegetation would compensate homeowners and groups caring about saguaros for a reallocation of resources toward greater protection of dispersed vegetation. Results highlight the importance of the spatial configuration of players and the resources they wish to protect in invasive species control problems.

Target Path Tracking Method of Intelligent Vehicle Based on Competitive Cooperative Game

To improve intelligent vehicle drive performance and avoid vehicle side-slip during target path tracking,a linearized four-wheel vehicle model is adopted as a predictive control model,and an intelligent ve-hicle target path tracking method based on a competitive cooperative game is proposed.The design variables are divided into different strategic spaces owned by each player by calculating the affecting factors of the design variables with objective functions and fuzzy clustering.Based on the competitive cooperative game model,each game player takes its payoff as a mono-objective to optimize its own strategic space and obtain the best strategy to deal with others.The best strategies were combined into the game strategy set.Considering the front wheel angle and side slip angle increment constraint,tire side-slip angle,and tire side slip deflection dynamics,it took the path tracking state model was used as the objective,function and the calculation was validated by competitive cooperative game theory.The results demonstrated the effectiveness of the proposed algorithm.The experimental results show that this method can track an intelligent vehicle quickly and steadily and has good real-time per-formance.

Cooperation influenced by the correlation degree of two-layered complex networks in evolutionary prisoner’s dilemma games

An evolutionary prisoner＇s dilemma game is investigated on two-layered complex networks respectively representing interaction and learning networks in one and two dimensions. A parameter q is introduced to denote the correlation degree between the two-layered networks. Using Monte Carlo simulations we studied the effects of the correlation degree on cooperative behaviour and found that the cooperator density nontrivially changes with q for different payoff parameter values depending on the detailed strategy updating and network dimension. An explanation for the obtained results is provided.

Cooperation and Phase Separation Driven by a Coevolving Snowdrift Game

We investigate the cooperative behavior and the phase separation in a coevolving system. Agents in the system constructed by a regular random network initially play the snowdrift game with their neighbors. They try to obtain a better competing environment by imitating a neighbor＇s more successful strategy or cutting the connection to a defective neighbor and randomly rewiring to another agent so as to seek a better neighborhood. The dynamic process of strategy imitation and relationship among agents due to rewiring neighbors may drive the system into different states. The simulation results show that there are three different phases in the q-r plane, where q is the rewiring probability and r is the cost-to-benefit ratio. One is a static phase of a pure cooperative cluster with a few isolated defectors. The other two belong to active phases with one of a main mixed-strategy cluster and the other of a pure defective state. We find that a simple mean field theory can predict correctly the static phase and the active phase of the main mixed-strategy cluster. The theoretical boundary line between the two phases is in good agreement with the simulation result.

A dynamic incentive and reputation mechanism for energy-efficient federated learning in 6G

As 5G becomes commercial,researchers have turned attention toward the Sixth-Generation(6G)network with the vision of connecting intelligence in a green energy-efficient manner.Federated learning triggers an upsurge of green intelligent services such as resources orchestration of communication infrastructures while preserving privacy and increasing communication efficiency.However,designing effective incentives in federated learning is challenging due to the dynamic available clients and the correlation between clients'contributions during the learning process.In this paper,we propose a dynamic incentive and reputation mechanism to improve energy efficiency and training performance of federated learning.The proposed incentive based on the Stackelberg game can timely adjust optimal energy consumption with changes in available clients during federated learning.Meanwhile,clients’contributions in reputation management are formulated based on the cooperative game to capture the correlation between tasks,which satisfies availability,fairness,and additivity.The simulation results show that the proposed scheme can significantly motivate high-performance clients to participate in federated learning and improve the accuracy and energy efficiency of the federated learning model.

Essential Players in Cooperative Games with Graph Communication Structure

A class of cooperative games with graph communication structure is studied in this paper by considering some important players,namely essential players.Under the assumption that only connected coalitions containing essential players are able to cooperate and obtain their worths,the class of graph games with essential players is proposed as well as an allocation rule.The proposed value follows the spirit of the Myerson value defined by applying the Shapley value on a modified game.Three properties,feasible component efficiency,the inessential component property,and fairness,are provided to fully characterize this value,where feasible component efficiency and fairness follows the same ideas of component efficiency and fairness for classical graph games,and the inessential component property says that the total payoffs of the players in a non-feasible component is zero.Moreover,some computational aspects of the proposed value and comparisons with disjunctive permission value for games with permission structure are also studied,respectively.