Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with firstorder and second-order players,respectively.In the developed algorithms,the observed disturbance values are included in control signals to eliminate the influence of disturbances,based on which a gradient-like optimization method is implemented for each player.Second,a signum function based distributed algorithm is proposed to attenuate disturbances for games with secondorder integrator-type players.To be more specific,a signum function is involved in the proposed seeking strategy to dominate disturbances,based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players'objective functions.Through Lyapunov stability analysis,it is proven that the players'actions can approach a small region around the Nash equilibrium by utilizing disturbance observerbased strategies with appropriate control gains.Moreover,exponential(asymptotic)convergence can be achieved when the signum function based control strategy(with an adaptive control gain)is employed.The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform(V-REP)and MATLAB.

A Matrix Approach to the Modeling and Analysis of Networked Evolutionary Games With Time Delays

Using the semi-tensor product method, this paper investigates the modeling and analysis of networked evolutionary games(NEGs) with finite memories, and presents a number of new results. Firstly, a kind of algebraic expression is formulated for the networked evolutionary games with finite memories, based on which the behavior of the corresponding evolutionary game is analyzed. Secondly, under a proper assumption, the existence of Nash equilibrium of the given networked evolutionary games is proved and a free-type strategy sequence is designed for the convergence to the Nash equilibrium. Finally, an illustrative example is worked out to support the obtained new results.

Evolutionary Games in Two-Layer Networks with the Introduction of Dominant Strategy

We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner＇s dilemma game （PDG） in one layer and snowdrift game （SDG） in the other. We explore the dependences of the fraction of the strategy cooperation in different layers on the game parameter and initial conditions. The results on two-layer square lattices show that, when cooperation is the dominant strategy, initial conditions strongly influence cooperation in the PDG layer while have no impact in the SDG layer. Moreover, in contrast to the result for PDG in single-layer square lattices, the parameter regime where cooperation could be maintained expands significantly in the PDG layer. We also investigate the effects of mutation and network topology. We find that different mutation rates do not change the cooperation behaviors. Moreover, similar behaviors on cooperation could be found in two-layer random networks.

A Game-Theoretic Approach to Elastic Control in Software-Defined Networking

Elastic control could balance the distributed control plane in Software-Defined Networking(SDN). Dynamic switch migration has been proposed to achieve it. However, existing schemes mainly focus on how to execute migration operation, but not why. This paper designs a decision-making mechanism based on zero-sum game theory to reelect a new controller as the master for migrated switches. It first chooses a switch for migration in the heavy controller which invites its neighbors as the game players to compete for the master role of this switch in the game-playing field(GPF) which is an occasional and loose domain for game-playing. Second, based on the concept of GPF, we design a decentralized strategy to play the game and determine which player as the final master. We implement it by extending the Open Flow protocol. Finally, numerical results demonstrate that our distributed strategy can approach elastic control plane with better performance.

A Game Theoretic Approach for Inter-Network Interference Mitigation in Wireless Body Area Networks

Wireless Body Area Network(WBAN) is an emerging technology to provide real-time health monitoring and ubiquitous healthcare services. In many applications, multiple wireless body area networks have to coexist in a small area, resulting in serious inter-network interference. This not only reduces network reliability that is especially important in emergency medical applications, but also consumes more power of WBANs. In this paper, an inter-network interference mitigation approach based on a power control algorithm is proposed. Power control is modeled as a non-cooperative game, in which both inter-network interference and energy efficiency of WBANs are considered. The existence and uniqueness of Nash Equilibrium in the game are proved, and an optimal scheme based on best response is proposed to find its Nash Equilibrium. By coordinating the transmission power levels among networks under interference environment, the total system throughput can be increased with minimum power consumed. The effectiveness of the proposed method has been illustrated by simulation results, where the performance of the proposed approach is evaluated in terms of overall utility and power efficiency and convergence speed.

Dual Power Allocation Optimization Based on Stackelberg Game in Heterogeneous Network with Hybrid Energy Supplies

In heterogeneous network with hybrid energy supplies including green energy and on-grid energy, it is imperative to increase the utilization of green energy as well as to improve the utilities of users and networks. As the difference of hybrid energy source in stability and economy, thus, this paper focuses on the network with hybrid energy source, and design the utility of each user in the hybrid energy source system from the perspective of stability, economy and environment pollution. A dual power allocation algorithm based on Stackelberg game to maximize the utilities of users and networks is proposed. In addition, an iteration method is proposed which enables all players to reach the Stackelberg equilibrium(SE). Simulation results validate that players can reach the SE and the utilities of users and networks can be maximization, and the green energy can be efficiently used.

Semi-tensor product approach to networked evolutionary games

In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.

Dynamics and Stability of Potential Hyper-networked Evolutionary Games

This paper considers the modeling and convergence of hyper-networked evolutionary games （HNEGs）. In an HNEG the network graph is a hypergraph, which allows the fundamental network game to be a multi-player one. Using semi-tensor product of matrices and the fundamental evolutionary equation, the dynamics of an HNEG is obtained and we extend the results about the networked evolutionary games to show whether an HNEG is potential and how to calculate the potential. Then we propose a new strategy updating rule, called the cascading myopic best response adjustment rule （MBRAR）, and prove that under the cascading MBRAR the strategies of an HNEG will converge to a pure Nash equilibrium. An example is presented and discussed in detail to demonstrate the theoretical and numerical results.

Stability Analysis of Networked Evolutionary Games with Profile-Dependent Delays

This paper investigates the networked evolutionary games(NEGs)with profile-dependent delays,including modeling and stability analysis.Profile-dependent delay,which varies with the game profiles,slows the information transmission between participants.Firstly,the dynamics model is proposed for the profile-dependent delayed NEG,then the algebraic formulation is established using the algebraic state space approach.Secondly,the dynamic behavior of the game is discussed,involving general stability and evolutionarily stable profile analysis.Necessary and sufficient criteria are derived using the matrices,which can be easily verified by mathematical software.Finally,a numerical example is carried out to demonstrate the validity of the theoretical results.

A Dynamic Network Game of the Fintech Industry

Economies of scale,economies of scope,and technology spillover are decisive eco-nomic elements that are crucial to the development in the Fintech industry.Thesepositive externalities are often realized through network links.In this paper,we presenta dynamic network offinancialfirms which exhibits these decisive elements.Thenetwork game equilibria are characterized.A Pareto efficient solution involving col-laboration of allfirms is provided.To obtain a fair-share distribution of cooperativegains,the Shapley value is adopted as the sharing mechanism.Payoff distributionmechanisms which guarantee the fulfilment of the Shapley value distribution in eachstage of the cooperation duration are derived.

Network Evolution Analysis of Vehicle Road-Driving Behavior Strategies and Design of Information Guidance Algorithm

By analyzing the influence of time and safety factors on the behavior strategies of vehicles on the road,a network game evolution model between drivers that considers the behavior strategies of the driving vehicle itself and its neighbors is constructed,and the competition relationship between different types of cars is studied.The influence of the proportion of driving vehicle types on the potential risk of the road is also discussed.This paper presents a guidance algorithm for vehicle dynamic behavior preference information.The correctness of the algorithm is verified by an example.Research shows:The choice of behavior strategies,such as speeding and lane changing,is related to the expected benefits of time,safety,and neighboring vehicle strategies,and the critical value of payable benefits is obtained.The higher the proportion of aggressive vehicles on the road,the greater the potential risk on the road.Whether there is a vehicle in the adjacent lane of the driving vehicle will affect the type of driving vehicle.Information guidance helps to stabilize the state of vehicles on the road,and the policy transition probability also helps stabilize the form of vehicles cars on the road.Still,information guidance has a more significant impact on the transition of vehicle types.Finally,the guidance strategy of managers is given when the road is smooth and congested.

Set Stability of Probabilistic Time-Delay Boolean Networks with Impulsive Effect

This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established for PTDBN with impulsive effect.Then,based on the probabilistic state transition matrix,a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect.Finally,the obtained new result is applied to the networked evolutionary game with memories.

Dynamic multicast sharing protection algorithm based on fuzzy game in multi-domain optical network

Aiming at the problem of dynamic multicast service protection in multi-domain optical network, this paper proposes a dynamic multicast sharing protection algorithm based on fuzzy game in multi-domain optical network. The algorithm uses the minimum cost spanning tree strategy and fuzzy game theory. First, it virtualizes two planes to calculate the multicast tree and the multicast protection tree respectively. Then, it performs a fuzzy game to form a cooperative alliance to optimize the path composition of each multicast tree. Finally, it generates a pair of optimal multicast work tree and multicast protection tree for dynamic multicast services. The time complexity of the algorithm is O(k3 m2 n), where n represents the number of nodes in the networks, k represents the number of dynamic multicast requests, and m represents the number of destination nodes for each multicast request. The experimental results show that the proposed algorithm reduces significantly the blocking rate of dynamic multicast services, and improves the utilization of optical network resources within a certain number of dynamic multicast request ranges.

A survey on potential evolutionary game and its applications

Basic concepts about the finite potential games and the networked evolutionary games(NEGs)are introduced.Some new developments are surveyed,including(i)formulas for verifying whether a finite game is(weighted)potential and for calculating the(weighted)potential function;and(ii)the fundamental network equation and strategy profile dynamics of NEGs.Then some applications are introduced,which include:(i)convergence of NEGs;(ii)congestion control;(iii)distributed coverage of graphs.