Since the carbon neutrality target was proposed,many countries have been facing severe challenges to carbon emission reduction sustainably.This study is conducted using a tripartite evolutionary game model to explore ...Since the carbon neutrality target was proposed,many countries have been facing severe challenges to carbon emission reduction sustainably.This study is conducted using a tripartite evolutionary game model to explore the impact of the central environmental protection inspection(CEPI)on driving carbon emission reduction,and to study what factors influence the strategic choices of each party and how they interact with each other.The research results suggest that local governments and manufacturing enterprises would choose strategies that are beneficial to carbon reduction when CEPI increases.When the initial willingness of all parties increases 20%,50%—80%,the time spent for the whole system to achieve stability decreases from 100%,60%—30%.The evolutionary result of“thorough inspection,regulation implementation,low-carbon management”is the best strategy for the tripartite evolutionary game.Moreover,the smaller the cost and the larger the benefit,the greater the likelihood of the three-party game stability strategy appears.This study has important guiding significance for other developing countries to promote carbon emission reduction by environmental policy.展开更多
Constructing a cross-border power energy system with multiagent power energy as an alliance is important for studying cross-border power-trading markets.This study considers multiple neighboring countries in the form ...Constructing a cross-border power energy system with multiagent power energy as an alliance is important for studying cross-border power-trading markets.This study considers multiple neighboring countries in the form of alliances,introduces neighboring countries’exchange rates into the cross-border multi-agent power-trading market and proposes a method to study each agent’s dynamic decision-making behavior based on evolutionary game theory.To this end,this study uses three national agents as examples,constructs a tripartite evolutionary game model,and analyzes the evolution process of the decision-making behavior of each agent member state under the initial willingness value,cost of payment,and additional revenue of the alliance.This research helps realize cross-border energy operations so that the transaction agent can achieve greater trade profits and provides a theoretical basis for cooperation and stability between multiple agents.展开更多
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...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.展开更多
Characteristics of knowledge exchanging behavior among individual agents in a knowledge dynamic interaction system are studied by using the game theory. An analytic model of evolutionary game of continuous dynamic kno...Characteristics of knowledge exchanging behavior among individual agents in a knowledge dynamic interaction system are studied by using the game theory. An analytic model of evolutionary game of continuous dynamic knowledge interaction behavior is founded based on the structure of the evolutionary game chain. Possible evolution trends of the model are discussed. Finally, evolutionary stable strategies （ESSs） of knowledge transactions among individual agents in the knowledge network are identified by simulation data. Stable charicteristics of ESS in a continuous knowledge exchanging team help employee to communicate and grasp the dynamic regulation of shared knowledge.展开更多
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 accumu...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.展开更多
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-mark...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.展开更多
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’...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.展开更多
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...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.展开更多
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 exp...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.展开更多
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 l...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.展开更多
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 nei...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.展开更多
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 g...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.展开更多
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 weight...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_0= 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).展开更多
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 uncondit...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.展开更多
The ubiquity of mobile devices have promoted the prosperity of mobile crowd systems, which recruit crowds to contribute their resources for performing tasks. Yet, due to the various resource consumption, the crowds ma...The ubiquity of mobile devices have promoted the prosperity of mobile crowd systems, which recruit crowds to contribute their resources for performing tasks. Yet, due to the various resource consumption, the crowds may be reluctant to join and contribute information. Thus, the low participation level of crowds will be a hurdle that prevents the adoption of crowdsourcing. A critical challenge for these systems is how to design a proper mechanism such that the crowds spontaneously act as suppliers to contribute accurate information. Most of existing mechanisms ignore either the honesty of crowds or requesters respectively. In this paper, considering the honesty of both, we propose a game-based incentive mechanism, namely RTRC, to stimulate the crowds to contribute accurate information and to motivate the requesters to return accurate feedbacks. In addition, an evolutionary game is designed to model the dynamic of user-strategy selection. Specially, the replicator dynamic is applied to model the adaptation of strategy interactions taking into account the dynamic nature in time dependence and we also derive the evolutionarily stable strategies(ESSs) for users. Finally, empirical results over the simulations show that all the requesters and suppliers will select honest strategy to maximize their profit.展开更多
Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner＇s Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optima...Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner＇s Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optimal control is designed for promoting cooperation based on the recent advances in mechanisms for the evolution of cooperation. Two con- trol strategies are proposed： compensation control strategy for the cooperator when playing against a defector and reward control strategy for cooperator when playing against a coop- erator. The feasibility and effectiveness of these control strategies for promoting cooperation in different stages are analyzed. The reward for cooperation can＇t prevent defection from being evolutionary stable strategy （ESS）. On the other hand, compensation for the coopera- tor can＇t prevent defection from emerging and sustaining. By considering the effect and the cost, an optimal control scheme with constraint on the admissible control set is put forward. By analyzing the special nonlinear system of replicator dynamics, the exact analytic solution of the optimal control scheme is obtained based on the maximum principle. Finally, the effectiveness of the proposed method is illustrated by examples.展开更多
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 t...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.展开更多
In this study,we propose a spatial prisoner＇s dilemma game model with a 2-stage strategy updating rule,and focus on the cooperation behavior of the system.In the first stage,i.e.,the pre-learning stage,a focal player...In this study,we propose a spatial prisoner＇s dilemma game model with a 2-stage strategy updating rule,and focus on the cooperation behavior of the system.In the first stage,i.e.,the pre-learning stage,a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors.If the player makes up his mind to update,he enters into the second stage,i.e.,the learning stage,and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule.The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor.Generally,the cooperation frequency decreases as the pre-learning factor increases;but a high cooperation level can be obtained in the intermediate region of- 3〈 β 〈-1.We then give some explanations via studying the co-action of pre-learning and learning.Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games.展开更多
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 ...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.展开更多
We adopt a floor field cellular automata model to study the statistical properties of bidirectional pedestrian flow movingin a straight corridor. We introduce a game-theoretic framework to deal with the conflict of mu...We adopt a floor field cellular automata model to study the statistical properties of bidirectional pedestrian flow movingin a straight corridor. We introduce a game-theoretic framework to deal with the conflict of multiple pedestrians tryingto move to the same target location. By means of computer simulations, we show that the complementary cumulative distributionof the time interval between two consecutive pedestrians leaving the corridor can be fitted by a stretched exponentialdistribution, and surprisingly, the statistical properties of the two types of pedestrian flows are affected differently by theflow ratio, i.e., the ratio of the pedestrians walking toward different directions. We also find that the jam probability exhibitsa non-monotonic behavior with the flow ratio, where the worst performance arises at an intermediate flow ratio of around0.2. Our simulation results are consistent with some empirical observations, which suggest that the peculiar characteristicsof the pedestrians may attributed to the anticipation mechanism of collision avoidance.展开更多
基金the financial support from the Postdoctoral Science Foundation of China(2022M720131)Spring Sunshine Collaborative Research Project of the Ministry of Education(202201660)+3 种基金Youth Project of Gansu Natural Science Foundation(22JR5RA542)General Project of Gansu Philosophy and Social Science Foundation(2022YB014)National Natural Science Foundation of China(72034003,72243006,and 71874074)Fundamental Research Funds for the Central Universities(2023lzdxjbkyzx008,lzujbky-2021-sp72)。
文摘Since the carbon neutrality target was proposed,many countries have been facing severe challenges to carbon emission reduction sustainably.This study is conducted using a tripartite evolutionary game model to explore the impact of the central environmental protection inspection(CEPI)on driving carbon emission reduction,and to study what factors influence the strategic choices of each party and how they interact with each other.The research results suggest that local governments and manufacturing enterprises would choose strategies that are beneficial to carbon reduction when CEPI increases.When the initial willingness of all parties increases 20%,50%—80%,the time spent for the whole system to achieve stability decreases from 100%,60%—30%.The evolutionary result of“thorough inspection,regulation implementation,low-carbon management”is the best strategy for the tripartite evolutionary game.Moreover,the smaller the cost and the larger the benefit,the greater the likelihood of the three-party game stability strategy appears.This study has important guiding significance for other developing countries to promote carbon emission reduction by environmental policy.
基金National Key R&D Program of China(Grant No.2022YFB2703500)National Natural Science Foundation of China(Grant No.52277104)+2 种基金National Key R&D Program of Yunnan Province(202303AC100003)Applied Basic Research Foundation of Yunnan Province (202301AT070455, 202101AT070080)Revitalizing Talent Support Program of Yunnan Province (KKRD202204024).
文摘Constructing a cross-border power energy system with multiagent power energy as an alliance is important for studying cross-border power-trading markets.This study considers multiple neighboring countries in the form of alliances,introduces neighboring countries’exchange rates into the cross-border multi-agent power-trading market and proposes a method to study each agent’s dynamic decision-making behavior based on evolutionary game theory.To this end,this study uses three national agents as examples,constructs a tripartite evolutionary game model,and analyzes the evolution process of the decision-making behavior of each agent member state under the initial willingness value,cost of payment,and additional revenue of the alliance.This research helps realize cross-border energy operations so that the transaction agent can achieve greater trade profits and provides a theoretical basis for cooperation and stability between multiple agents.
基金Project supported by the Doctoral Foundation Project of Guizhou University(Grant No.(2019)49)the National Natural Science Foundation of China(Grant No.71961003)the Science and Technology Program of Guizhou Province(Grant No.7223)。
文摘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.
文摘Characteristics of knowledge exchanging behavior among individual agents in a knowledge dynamic interaction system are studied by using the game theory. An analytic model of evolutionary game of continuous dynamic knowledge interaction behavior is founded based on the structure of the evolutionary game chain. Possible evolution trends of the model are discussed. Finally, evolutionary stable strategies （ESSs） of knowledge transactions among individual agents in the knowledge network are identified by simulation data. Stable charicteristics of ESS in a continuous knowledge exchanging team help employee to communicate and grasp the dynamic regulation of shared knowledge.
基金supported by the National Natural Science Foundation of China (Grant No. 71071119)the Fundamental Research Funds for the Central Universities
文摘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.
基金supported by the National Key R&D Program of China(2017YFB0902200).
文摘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.
基金supported by the Fund of Education Ministry Humanity and Society (No. 18YJCZH016)
文摘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.
基金supported by the National Natural Science Foundation of China(71871171,72031009)。
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grand No. 10575055)K. C. Wong Magna Fund in Ningbo University
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11575036,71301012,and 11505016
文摘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.
基金Project supported by the CAS/USTC Special Grant for Postgraduate Research,Innovation,and Practice
文摘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.
基金the National Natural Science Foun-dation of China(Grant No.71961003).
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575072 and 11475074)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2017-172)
文摘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_0= 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).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11175131 and 10875086)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61672408, U1405255, 61502368, 61602537, 61602357, 61672413, U1509214, U1135002)National High Technology Research and Development Program (863 Program) (Grant Nos. 2015AA016007, 2015AA017203)+5 种基金China Postdoctoral Science Foundation Funded Project (Grant No.2016M592762)Shaanxi Science & Technology Coordination & Innovation Project (Grant No.2016TZC-G-6-3)Shaanxi Provincial Natural Science Foundation (Grant Nos. 2015JQ6227, 2016JM6005)China 111 Project (Grant No. B16037)Beijing Municipal Social Science Foundation(Grant No. 16XCC023)Fundamental Research Funds for the Central Universities (Grant Nos. JB150308, JB150309, JB161501, JBG161511)
文摘The ubiquity of mobile devices have promoted the prosperity of mobile crowd systems, which recruit crowds to contribute their resources for performing tasks. Yet, due to the various resource consumption, the crowds may be reluctant to join and contribute information. Thus, the low participation level of crowds will be a hurdle that prevents the adoption of crowdsourcing. A critical challenge for these systems is how to design a proper mechanism such that the crowds spontaneously act as suppliers to contribute accurate information. Most of existing mechanisms ignore either the honesty of crowds or requesters respectively. In this paper, considering the honesty of both, we propose a game-based incentive mechanism, namely RTRC, to stimulate the crowds to contribute accurate information and to motivate the requesters to return accurate feedbacks. In addition, an evolutionary game is designed to model the dynamic of user-strategy selection. Specially, the replicator dynamic is applied to model the adaptation of strategy interactions taking into account the dynamic nature in time dependence and we also derive the evolutionarily stable strategies(ESSs) for users. Finally, empirical results over the simulations show that all the requesters and suppliers will select honest strategy to maximize their profit.
文摘Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner＇s Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optimal control is designed for promoting cooperation based on the recent advances in mechanisms for the evolution of cooperation. Two con- trol strategies are proposed： compensation control strategy for the cooperator when playing against a defector and reward control strategy for cooperator when playing against a coop- erator. The feasibility and effectiveness of these control strategies for promoting cooperation in different stages are analyzed. The reward for cooperation can＇t prevent defection from being evolutionary stable strategy （ESS）. On the other hand, compensation for the coopera- tor can＇t prevent defection from emerging and sustaining. By considering the effect and the cost, an optimal control scheme with constraint on the admissible control set is put forward. By analyzing the special nonlinear system of replicator dynamics, the exact analytic solution of the optimal control scheme is obtained based on the maximum principle. Finally, the effectiveness of the proposed method is illustrated by examples.
基金Supported by National Natural Science Foundation of China(71231007,50909073)
文摘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.
基金Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y1110766,Y1101316,Y6110317,and LY12A05003)the Key Science and Technology Plan Program of Zhejiang Province,China (Grant No. 2010C13021)
文摘In this study,we propose a spatial prisoner＇s dilemma game model with a 2-stage strategy updating rule,and focus on the cooperation behavior of the system.In the first stage,i.e.,the pre-learning stage,a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors.If the player makes up his mind to update,he enters into the second stage,i.e.,the learning stage,and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule.The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor.Generally,the cooperation frequency decreases as the pre-learning factor increases;but a high cooperation level can be obtained in the intermediate region of- 3〈 β 〈-1.We then give some explanations via studying the co-action of pre-learning and learning.Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games.
基金Project supported by the National Natural Science Foundation of China(Grant No.61963013).
文摘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.
基金the National Natural Science Founda-tion of China(Grant Nos.11975111 and 12247101)the 111 Project(Grant No.B20063)the Fundamental Research Funds for the Central Universities of Ministry of Education of China(Grant Nos.lzujbky-2019-85,lzujbky-2023-ey02,and lzujbky-2024-11).
文摘We adopt a floor field cellular automata model to study the statistical properties of bidirectional pedestrian flow movingin a straight corridor. We introduce a game-theoretic framework to deal with the conflict of multiple pedestrians tryingto move to the same target location. By means of computer simulations, we show that the complementary cumulative distributionof the time interval between two consecutive pedestrians leaving the corridor can be fitted by a stretched exponentialdistribution, and surprisingly, the statistical properties of the two types of pedestrian flows are affected differently by theflow ratio, i.e., the ratio of the pedestrians walking toward different directions. We also find that the jam probability exhibitsa non-monotonic behavior with the flow ratio, where the worst performance arises at an intermediate flow ratio of around0.2. Our simulation results are consistent with some empirical observations, which suggest that the peculiar characteristicsof the pedestrians may attributed to the anticipation mechanism of collision avoidance.
