Evolutionary game dynamics of combining two different aspiration-driven update rules in structured populations

In evolutionary games,most studies on finite populations have focused on a single updating mechanism.However,given the differences in individual cognition,individuals may change their strategies according to different updating mechanisms.For this reason,we consider two different aspiration-driven updating mechanisms in structured populations:satisfied-stay unsatisfied shift(SSUS)and satisfied-cooperate unsatisfied defect(SCUD).To simulate the game player’s learning process,this paper improves the particle swarm optimization algorithm,which will be used to simulate the game player’s strategy selection,i.e.,population particle swarm optimization(PPSO)algorithms.We find that in the prisoner’s dilemma,the conditions that SSUS facilitates the evolution of cooperation do not enable cooperation to emerge.In contrast,SCUD conditions that promote the evolution of cooperation enable cooperation to emerge.In addition,the invasion of SCUD individuals helps promote cooperation among SSUS individuals.Simulated by the PPSO algorithm,the theoretical approximation results are found to be consistent with the trend of change in the simulation results.

Dynamic Evolutionary Game-based Modeling,Analysis and Performance Enhancement of Blockchain Channels

The recent development of channel technology has promised to reduce the transaction verification time in blockchain operations.When transactions are transmitted through the channels created by nodes,the nodes need to cooperate with each other.If one party refuses to do so,the channel is unstable.A stable channel is thus required.Because nodes may show uncooperative behavior,they may have a negative impact on the stability of such channels.In order to address this issue,this work proposes a dynamic evolutionary game model based on node behavior.This model considers various defense strategies'cost and attack success ratio under them.Nodes can dynamically adjust their strategies according to the behavior of attackers to achieve their effective defense.The equilibrium stability of the proposed model can be achieved.The proposed model can be applied to general channel networks.It is compared with two state-of-the-art blockchain channels:Lightning network and Spirit channels.The experimental results show that the proposed model can be used to improve a channel's stability and keep it in a good cooperative stable state.Thus its use enables a blockchain to enjoy higher transaction success ratio and lower transaction transmission delay than the use of its two peers.

Evolutionary privacy-preserving learning strategies for edge-based IoT data sharing schemes

The fast proliferation of edge devices for the Internet of Things(IoT)has led to massive volumes of data explosion.The generated data is collected and shared using edge-based IoT structures at a considerably high frequency.Thus,the data-sharing privacy exposure issue is increasingly intimidating when IoT devices make malicious requests for filching sensitive information from a cloud storage system through edge nodes.To address the identified issue,we present evolutionary privacy preservation learning strategies for an edge computing-based IoT data sharing scheme.In particular,we introduce evolutionary game theory and construct a payoff matrix to symbolize intercommunication between IoT devices and edge nodes,where IoT devices and edge nodes are two parties of the game.IoT devices may make malicious requests to achieve their goals of stealing privacy.Accordingly,edge nodes should deny malicious IoT device requests to prevent IoT data from being disclosed.They dynamically adjust their own strategies according to the opponent's strategy and finally maximize the payoffs.Built upon a developed application framework to illustrate the concrete data sharing architecture,a novel algorithm is proposed that can derive the optimal evolutionary learning strategy.Furthermore,we numerically simulate evolutionarily stable strategies,and the final results experimentally verify the correctness of the IoT data sharing privacy preservation scheme.Therefore,the proposed model can effectively defeat malicious invasion and protect sensitive information from leaking when IoT data is shared.

Adaptive dynamic reconfiguration mechanism of unmanned swarm topology based on an evolutionary game

Autonomous cooperation of unmanned swarms is the research focus on“new combat forces”and“disruptive technologies”in military fields.The mechanism design is the fundamental way to realize autonomous cooperation.Facing the realistic requirements of a swarm network dynamic adjustment under the background of high dynamics and strong confrontation and aiming at the optimization of the coordination level,an adaptive dynamic reconfiguration mechanism of unmanned swarm topology based on an evolutionary game is designed.This paper analyzes military requirements and proposes the basic framework of autonomous cooperation of unmanned swarms,including the emergence of swarm intelligence,information network construction and collaborative mechanism design.Then,based on the framework,the adaptive dynamic reconfiguration mechanism is discussed in detail from two aspects:topology dynamics and strategy dynamics.Next,the unmanned swarms’community network is designed,and the network characteristics are analyzed.Moreover,the mechanism characteristics are analyzed by numerical simulation,focusing on the impact of key parameters,such as cost,benefit coefficient and adjustment rate on the level of swarm cooperation.Finally,the conclusion is made,which is expected to provide a theoretical reference and decision support for cooperative mode design and combat effectiveness generation of unmanned swarm operations.

Evolutionary game-based optimization of green certificate-carbon emission right-electricity joint market for thermal-wind-photovoltaic power system

With the increasing proportion of renewable energy in the power market,the demands on government financial subsidies are gradually increasing.Thus,a joint green certificate-carbon emission right-electricity multi-market trading process is proposed to study the market-based strategy for renewable energy.Considering the commodity characteristics of green certificates and carbon emission rights,the dynamic cost models of green certificates and carbon rights are constructed based on the Rubinstein game and ladder pricing models.Furthermore,considering the irrational bidding behavior of energy suppliers in the actual electricity market,an evolutionary game based multi-market bidding optimization model is presented.Subsequently,it is solved using a composite differential evolutionary algorithm.Finally,the case study results reveal that the proposed model can increase profits and the consumption rate of renewable energy and reduce carbon emission.

Adaptive interaction driven by the learning effect in the spatial prisoner's dilemma

We propose a computing model in which individuals can automatically adjust their interaction intensity with their mentor according to the learning effect.This model is designed to investigate the cooperative dynamics of the spatial prisoner's dilemma.More specifically,when the cumulative payoff of a learner is more than his reference earning,he will strengthen his interaction with his mentor;otherwise,he will reduce it.The experimental results indicate that this mechanism can improve the emergence of cooperation in a networked population and that the driving coefficient of interaction intensity plays an important role in promoting cooperation.Interestingly,under a certain social dilemma condition,there exists a minimal driving coefficient that leads to optimal cooperation.This occurs due to a positive feedback effect between the individual's satisfaction frequency and the number of effective neighbors.Moreover,we find that the experimental results are in accord with theoretical predictions obtained from an extension of the classical pair-approximation method.Our conclusions obtained by considering relationships with mentors can provide a new perspective for future investigations into the dynamics of evolutionary games within structured populations.

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 a generalized Moran process with arbitrary selection strength and mutation

By using a generalized fitness-dependent Moran process, an evolutionary model for symmetric 2 × 2 games in a well-mixed population with a finite size is investigated. In the model, the individuals＇ payoff accumulating from games is mapped into fitness using an exponent function. Both selection strength β and mutation rate ε are considered. The process is an ergodic birth-death process. Based on the limit distribution of the process, we give the analysis results for which strategy will be favoured when s is small enough. The results depend on not only the payoff matrix of the game, but also on the population size. Especially, we prove that natural selection favours the strategy which is risk-dominant when the population size is large enough. For arbitrary β and ε values, the ＇Hawk-Dove＇ game and the ＇Coordinate＇ game are used to illustrate our model. We give the evolutionary stable strategy （ESS） of the games and compare the results with those of the replicator dynamics in the infinite population. The results are determined by simulation experiments.

Evolutionary game analysis between the government and the waste producer in the venous industry

The relationship between the government and the waste producer is always a representative and realistic issue,especially concerning the venous industry.This article is based on the true relationship between the government and the waste producer,uses the methods from the evolutionary game theory,and analyzes the relationship between the government and the waste producer in detail.

A single-task and multi-decision evolutionary game model based on multi-agent reinforcement learning

In the evolutionary game of the same task for groups,the changes in game rules,personal interests,the crowd size,and external supervision cause uncertain effects on individual decision-making and game results.In the Markov decision framework,a single-task multi-decision evolutionary game model based on multi-agent reinforcement learning is proposed to explore the evolutionary rules in the process of a game.The model can improve the result of a evolutionary game and facilitate the completion of the task.First,based on the multi-agent theory,to solve the existing problems in the original model,a negative feedback tax penalty mechanism is proposed to guide the strategy selection of individuals in the group.In addition,in order to evaluate the evolutionary game results of the group in the model,a calculation method of the group intelligence level is defined.Secondly,the Q-learning algorithm is used to improve the guiding effect of the negative feedback tax penalty mechanism.In the model,the selection strategy of the Q-learning algorithm is improved and a bounded rationality evolutionary game strategy is proposed based on the rule of evolutionary games and the consideration of the bounded rationality of individuals.Finally,simulation results show that the proposed model can effectively guide individuals to choose cooperation strategies which are beneficial to task completion and stability under different negative feedback factor values and different group sizes,so as to improve the group intelligence level.

Medium and long-term thermal coal contract embedded reparations from the perspective of an evolutionary game

Coal-fired electricity enterprises are caught in the dilemma of relative fixed prices and rising costs under the scenario of decarbonization.Meanwhile,soaring market-oriented coal pricing results in coal enterprises’increasing defaults on thermal coal medium-and long-term contracts(MLC).To investigate the implementation of MLC at the micro-level,this study formalized the contractual behaviors of coal and coal-fired electricity enterprises based on the asymmetric evolutionary game.We formalized the evolving behaviors of both parties using replicator dynamics equations and proved that there were two evolutionary stabilization strategies(ESSs):compliance and coal enterprises’unilateral default.A multi-agent-based simulation was applied to verify the evolving process of ESSs and determine the critical values of MLC design by sensitive analysis.From the simulation results,coal-fired electricity enterprises do not stop generation under the current carbon quota allocation mechanism,even if carbon emission trading increases electricity generation costs.Coal enterprises choose to“default”when the market price of coal is higher than the contracted price by 18%.However,if the original reparation is increased by 5%,the compliance rate of the coal enterprises improves.Dynamic reparations embedded in the MLC improved enforcement during the contracting period.Moreover,the proposed policy implications have practical significance for enhancing the coordinated operation of coal-electricity energy supply chains.

EVOLUTIONARY DYNAMICS ON ONE-DIMENSIONAL CYCLE WITH SHIFTING MECHANISM AND TINY MUTATION RATE

In this paper we study the impact of tiny mutation on the evolutionary dynamics on one-dimensional cycle with shifting mechanism. The evolutionary success is evaluated by investigating the stationary distribution of the ergodic process with the idea of viscosity solutions. The cooperative behaviors in ecosystem and social system are briefly discussed by applying the results to the prisoner＇s dilemma game.

Evolutionary game analysis of problem processing mechanism in new collaboration

This paper analyzes a problem processing mechanism in a new collaboration system between the main manufacturer and the supplier in the"main manufacturer-supplier"mode,which has been widely applied in the collaborative development management of the complex product.This paper adopts the collaboration theory,the evolutionary game theory and numerical simulation to analyze the decision-making mechanism where one upstream supplier and one downstream manufacturer must process an unpredicted problem without any advance contract in common.Results show that both players'decision-makings are in some correlation with the initial state,income impact coefficients,and dealing cost.It is worth noting that only the initial state influences the final decision,while income impact coefficients and dealing cost just influence the decision process.This paper shows reasonable and practical suggestions for the manufacturer and supplier in a new collaboration system for the first time and is dedicated to the managerial implications on reducing risks of processing problems.

Effects of the planarity and heterogeneity of networks on evolutionary two-player games

We study the effects of the planarity and heterogeneity of networks on evolutionary two-player symmetric games by considering four different kinds of networks, including two types of heterogeneous networks: the weighted planar stochastic lattice（a planar scale-free network） and the random uncorrelated scale-free network with the same degree distribution as the weighted planar stochastic lattice; and two types of homogeneous networks: the hexagonal lattice and the random regular network with the same degree k;= 6 as the hexagonal lattice. Using extensive computer simulations, we found that both the planarity and heterogeneity of the network have a significant influence on the evolution of cooperation, either promotion or inhibition, depending not only on the specific kind of game（the Harmony, Snowdrift, Stag Hunt or Prisoner’s Dilemma games）, but also on the update rule（the Fermi, replicator or unconditional imitation rules）.

THE AVERAGE ABUNDANCE FUNCTION WITH MUTATION OF THE MULTI-PLAYER SNOWDRIFT EVOLUTIONARY GAME MODEL

This article explores the characteristics of the average abundance function with mutation on the basis of the multi-player snowdrift evolutionary game model by analytical analysis and numerical simulation.The specific field of this research concerns the approximate expressions of the average abundance function with mutation on the basis of different levels of selection intensity and an analysis of the results of numerical simulation on the basis of the intuitive expression of the average abundance function.In addition,the biological background of this research lies in research on the effects of mutation,which is regarded as a biological concept and a disturbance to game behavior on the average abundance function.The mutation will make the evolutionary result get closer to the neutral drift state.It can be deduced that this affection is not only related to mutation,but also related to selection intensity and the gap between payoff and aspiration level.The main research findings contain four aspects.First,we have deduced the concrete expression of the expected payoff function.The asymptotic property and change trend of the expected payoff function has been basically obtained.In addition,the intuitive expression of the average abundance function with mutation has been obtained by taking the detailed balance condition as the point of penetration.It can be deduced that the effect of mutation is to make the average abundance function get close to 1/2.In addition,this affection is related to selection intensity and the gap.Secondly,the first-order Taylor expansion of the average abundance function has been deduced for when selection intensity is sufficiently small.The expression of the average abundance function with mutation can be simplified from a composite function to a linear function because of this Taylor expansion.This finding will play a significant role when analyzing the results of the numerical simulation.Thirdly,we have obtained the approximate expressions of the average abundance function corresponding to small and large selection intensity.The significance of the above approximate analysis lies in that we have grasped the basic characteristics of the effect of mutation.The effect is slight and can be neglected when mutation is very small.In addition,the effect begins to increase when mutation rises,and this effect will become more remarkable with the increase of selection intensity.Fourthly,we have explored the influences of parameters on the average abundance function with mutation through numerical simulation.In addition,the corresponding results have been explained on the basis of the expected payoff function.It can be deduced that the influences of parameters on the average abundance function with mutation will be slim when selection intensity is small.Moreover,the corresponding explanation is related to the first-order Taylor expansion.Furthermore,the influences will become notable when selection intensity is large.

Exploring the dynamic evolutionary mechanism of game model on the protection of traditional villages

With the rapid improvement of urbanization and industrialization in countries around the world,how to effectively solve the rapid demise of traditional villages is a social dilemma faced by all countries,which is why a series of relevant protection regulations have been promulgated in different historical periods.However,the formulation of relevant policies is still not scientific,universal,and long-term.In this study,we constructed an evolutionary game model of local governments and residents based on the evolutionary game theory(EGT),which is used to explore the evolutionary stability strategy(ESS)and stability conditions of stakeholders under the premise of mutual influence and restriction.Besides,the study also included the analysis about the impacts of different influence factors on the evolution tendency of the game model.At the same time,numerical simulation examples were used to verify the theoretical results and three crucial conclusions have been drawn.Firstly,the strategic evolution of stakeholders is a dynamic process of continuous adjustment and optimization,and its results and speed show consistent interdependence.Secondly,the decision-making of stakeholders mainly depends on the basic cost,and the high cost of investment is not conducive to the protection of traditional villages.Thirdly,the dynamic evolutionary mechanism composed of different influence factors will have an impact on the direction and speed of decision-making of stakeholders,which provides the basis for them to effectively restrict the decision-making of each other.This study eliminates the weaknesses of existing research approaches and provides scientific and novel ideas for the protection of traditional villages,which can contribute to the formulation and improvement of the relevant laws and regulations.

Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model

We investigate a simple evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the b payoff of a defector exploiting a cooperator is small. Furthermore, if b is large enough, then the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is roughly estimated. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.

Integrating the environmental factor into the strategy updating rule to promote cooperation in evolutionary games

Many previous studies have shown that the environment plays an important role for social individuals. In this paper, we integrate the environmental factor, which is defined as the average payoff of all a player＇s neighbours, with the standard Fermi updating rule by introducing a tunable parameter, w. It is found that the level of cooperation increases remarkably, and that the cooperators can better resist the invasion of defection with an increase in w. This interesting phenomenon is then explained from a microscopic view. In addition, the universality of this mechanism is also proved with the help of the small-world network and the random regular graph. This work may be helpful in understanding cooperation behaviour in species from unicellular organisms up to human beings.

Spatial snowdrift game in heterogeneous agent systems with co-evolutionary strategies and updating rules

We propose an evolutionary snowdrift game model for heterogeneous systems with two types of agents, in which the inner-directed agents adopt the memory-based updating rule while the copycat-like ones take the unconditional imitation rule; moreover, each＇agent can change his type to adopt another updating rule once the number he sequentially loses the game at is beyond his upper limit of tolerance. The cooperative behaviors of such heterogeneous systems are then investigated by Monte Carlo simulations. The numerical results show the equilibrium cooperation frequency and composition as functions of the cost-to-benefit ratio r are both of plateau structures with discontinuous steplike jumps, and the number of plateaux varies non-monotonically with the upper limit of tolerance VT as well as the initial composition of agents faO. Besides, the quantities of the cooperation frequency and composition are dependent crucially on the system parameters including VT, faO, and r. One intriguing observation is that when the upper limit of tolerance is small, the cooperation frequency will be abnormally enhanced with the increase of the cost-to-benefit ratio in the range of 0 〈 r 〈 1/4. We then probe into the relative cooperation frequencies of either type of agents, which are also of plateau structures dependent on the system parameters. Our results may be helpful to understand the cooperative behaviors of heterogenous agent systems.

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.