The livestock farming is an important pillar of the rural economy in China.To explore the impact of government technical subsidies and pollution penalties on the digital and intelligent transformation of livestock ent...The livestock farming is an important pillar of the rural economy in China.To explore the impact of government technical subsidies and pollution penalties on the digital and intelligent transformation of livestock enterprises,an evolutionary game theoretical model between the government and livestock enterprises is constructed.The interaction mechanism of the game between the government and breeding enterprises is explored,and simulation is conducted.The research results show that the combined strategy of pollution penalties and technical subsidies is the optimal strategy for the government;the system is jointly driven by government subsidies,technical costs of transformation input,public willingness,and enterprise willingness.展开更多
The proof-of-stake(PoS)mechanism is a consensus protocol within blockchain technology that determines the validation of transactions and the minting of new blocks based on the participant’s stake in the cryptocurrenc...The proof-of-stake(PoS)mechanism is a consensus protocol within blockchain technology that determines the validation of transactions and the minting of new blocks based on the participant’s stake in the cryptocurrency network.In contrast to proof-of-work(PoW),which relies on computational power to validate transactions,PoS employs a deterministic and resourceefficient approach to elect validators.Whereas,an inherent risk of PoS is the potential for centralization among a small cohort of network participants possessing substantial stakes,jeopardizing system decentralization and posing security threats.To mitigate centralization issues within PoS,this study introduces an incentive-aligned mechanism named decentralized proof-of-stake(DePoS),wherein the second-largest stakeholder is chosen as the final validator with a higher probability.Integrated with the verifiable random function(VRF),DePoS rewards the largest stakeholder with uncertainty,thus disincentivizing stakeholders from accumulating the largest stake.Additionally,a dynamic evolutionary game model is innovatively developed to simulate the evolution of staking pools,thus facilitating the investigation of staking pool selection dynamics and equilibrium stability across PoS and DePoS systems.The findings demonstrate that DePoS generally fosters wealth decentralization by discouraging the accumulation of significant cryptocurrency holdings.Through theoretical analysis of stakeholder predilection in staking pool selection and the simulation of the evolutionary tendency in pool scale,this research demonstrates the comparative advantage in decentralization offered by DePoS over the conventional PoS.展开更多
The green retrofit of existing public buildings is a necessary choice to promote energy conservation,emission reduction,and sustainable development goals in the construction industry,and to advance the implementation ...The green retrofit of existing public buildings is a necessary choice to promote energy conservation,emission reduction,and sustainable development goals in the construction industry,and to advance the implementation of the national"carbon peaking and carbon neutrality"strategy.The effective governance of green retrofit projects for existing public buildings essentially involves a dynamic process of repeated strategic interactions among key stakeholders.From the perspective of project governance,this study clarifies the game-theoretic relationship between ESCO and owners under government guidance,and constructs an evolutionary game model involving the government,ESCO,and owners.The study explores the strategic choices of the core stakeholders in the green retrofit projects of existing public buildings.The aim is to lay a foundation for research on the decision-making coordination and implementation mechanisms between ESCO and owners,thus promoting the efficient and healthy development of green retrofit projects for existing public buildings.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
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, wh...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.展开更多
One of the assumptions of previous research in evolutionary game dynamics is that individuals use only one rule to update their strategy. In reality, an individual's strategy update rules may change with the envir...One of the assumptions of previous research in evolutionary game dynamics is that individuals use only one rule to update their strategy. In reality, an individual's strategy update rules may change with the environment, and it is possible for an individual to use two or more rules to update their strategy. We consider the case where an individual updates strategies based on the Moran and imitation processes, and establish mixed stochastic evolutionary game dynamics by combining both processes. Our aim is to study how individuals change strategies based on two update rules and how this affects evolutionary game dynamics. We obtain an analytic expression and properties of the fixation probability and fixation times(the unconditional fixation time or conditional average fixation time) associated with our proposed process. We find unexpected results. The fixation probability within the proposed model is independent of the probabilities that the individual adopts the imitation rule update strategy. This implies that the fixation probability within the proposed model is equal to that from the Moran and imitation processes. The one-third rule holds in the proposed mixed model. However, under weak selection, the fixation times are different from those of the Moran and imitation processes because it is connected with the probability that individuals adopt an imitation update rule. Numerical examples are presented to illustrate the relationships between fixation times and the probability that an individual adopts the imitation update rule, as well as between fixation times and selection intensity. From the simulated analysis, we find that the fixation time for a mixed process is greater than that of the Moran process, but is less than that of the imitation process. Moreover, the fixation times for a cooperator in the proposed process increase as the probability of adopting an imitation update increases; however, the relationship becomes more complex than a linear relationship.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
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 ex...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.展开更多
Traditional evolutionary games assume uniform interaction rate, which means that the rate at which individuals meet and interact is independent of their strategies. But in some systems, especially biological systems, ...Traditional evolutionary games assume uniform interaction rate, which means that the rate at which individuals meet and interact is independent of their strategies. But in some systems, especially biological systems, the players interact with each other discriminately. Taylor and Nowak (2006) were the first to establish the corresponding non-uniform interaction rate model by allowing the interaction rates to depend on strategies. Their model is based on replicator dynamics which assumes an infinite size population. But in reality, the number of individuals in the population is always finite, and there will be some random interference in the individuals' strategy selection process. Therefore, it is more practical to establish the corresponding stochastic evolutionary model in finite populations. In fact, the analysis of evolutionary games in a finite size population is more difficult. Just as Taylor and Nowak said in the outlook section of their paper, 'The analysis of non-uniform interaction rates should be extended to stochastic game dynamics of finite populations.' In this paper, we are exactly doing this work. We extend Taylor and Nowak's model from infinite to finite case, especially focusing on the influence of non-uniform connection characteristics on the evolutionary stable state of the system. We model the strategy evolutionary process of the population by a continuous ergodic Markov process. Based on the limit distribution of the process, we can give the evolutionary stable state of the system. We make a complete classification of the symmetric 2×2 games. For each case game, the corresponding limit distribution of the Markov-based process is given when noise intensity is small enough. In contrast with most literatures in evolutionary games using the simulation method, all our results obtained are analytical. Especially, in the dominant-case game, coexistence of the two strategies may become evolutionary stable states in our model. This result can be used to explain the emergence of cooperation in the Prisoner is Dilemma Games to some extent. Some specific examples are given to illustrate our results.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
Personalized products and services in e-commerce bring consumers many new experiences, but also trigger a series of information security issues. Considering the bounded rationality of the game participants, in this pa...Personalized products and services in e-commerce bring consumers many new experiences, but also trigger a series of information security issues. Considering the bounded rationality of the game participants, in this paper, we propose an evolutionary game model of privacy protection between firms and consumers based on e-commerce personalization. Evolutionary stable strategies（ESSs） are obtained from the equilibrium points according to the model analysis, and then simulation experiments are launched to validate the decision-making results and the influencing mechanism of various factors. The results show that the model can eventually evolve toward a win-win situation by wisely varying its various factors, such as ratios of initial strategies, cost of privacy protection, commodity prices, and other related factors. Further, we find that reducing the possibility of the privacy breach under the premise of privacy protection can help promote the e-commerce personalization.展开更多
Evolutionary game dynamics in finite size populations can be described by a fitness-dependent Wright- Fisher process. We consider symmetric 2×2 games in a well-mixed population. In our model, two parameters to de...Evolutionary game dynamics in finite size populations can be described by a fitness-dependent Wright- Fisher process. We consider symmetric 2×2 games in a well-mixed population. In our model, two parameters to describe the level of player＇s rationality and noise intensity in environment are introduced. In contrast with the fixation probability method that used in a noiseless case, the introducing of the noise intensity parameter makes the process an ergodic Markov process and based on the limit distribution of the process, we can analysis the evolutionary stable strategy （ESS） of the games. We illustrate the effects of the two parameters on the ESS of games using the Prisoner＇s dilemma games （PDG） and the snowdrift games （SG）. We also compare the ESS of our model with that of the replicator dynamics in infinite size populations. The results are determined by simulation experiments.展开更多
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. Usin...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.展开更多
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 govern...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.展开更多
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 M...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.展开更多
In order to protect the interests of electric vehicle users and grid companies with vehicle-to-grid(V2G)technology,a reasonable electric vehicle discharge electricity price is established through the evolutionary game...In order to protect the interests of electric vehicle users and grid companies with vehicle-to-grid(V2G)technology,a reasonable electric vehicle discharge electricity price is established through the evolutionary game model.A game model of power grid companies and electric vehicle users based on the evolutionary game theory is established to balance the revenue of both players in the game.By studying the dynamic evolution process of both sides of the game,the range of discharge price that satisfies the interests of both sides is obtained.The results are compared with those obtained by the static Bayesian game.The results show that the discharge price which can benefit both sides of the game exists in a specific range.According to the setting of the example,the reasonable discharge electricity price is 1.1060 to 1.4811 yuan/(kW·h).Only within this range can the power grid company and electric vehicle users achieve positive interactions.In addition,the evolutionary game model is easier to balance the interests of the two players than the static Bayesian game.展开更多
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 ...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.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
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.Fac...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.展开更多
To satisfy mobile terminals ’( MTs) offloading requirements and reduce MTs’ cost,a joint cloud and wireless resource allocation scheme based on the evolutionary game( JRA-EG) is proposed for overlapping heterogeneou...To satisfy mobile terminals ’( MTs) offloading requirements and reduce MTs’ cost,a joint cloud and wireless resource allocation scheme based on the evolutionary game( JRA-EG) is proposed for overlapping heterogeneous networks in mobile edge computing environments. MTs that have tasks offloading requirements in the same service area form a population. MTs in one population acquire different wireless and computation resources by selecting different service providers( SPs). An evolutionary game is formulated to model the SP selection and resource allocation of the MTs. The cost function of the game consists of energy consumption,time delay and monetary cost. The solutions of evolutionary equilibrium( EE) include the centralized algorithm based on replicator dynamics and the distributed algorithm based on Q-learning.Simulation results show that both algorithms can converge to the EE rapidly. The differences between them are the convergence speed and trajectory stability. Compared with the existing schemes,the JRA-EG scheme can save more energy and have a smaller time delay when the data size becomes larger. The proposed scheme can schedule the wireless and computation resources reasonably so that the offloading cost is reduced efficiently.展开更多
文摘The livestock farming is an important pillar of the rural economy in China.To explore the impact of government technical subsidies and pollution penalties on the digital and intelligent transformation of livestock enterprises,an evolutionary game theoretical model between the government and livestock enterprises is constructed.The interaction mechanism of the game between the government and breeding enterprises is explored,and simulation is conducted.The research results show that the combined strategy of pollution penalties and technical subsidies is the optimal strategy for the government;the system is jointly driven by government subsidies,technical costs of transformation input,public willingness,and enterprise willingness.
文摘The proof-of-stake(PoS)mechanism is a consensus protocol within blockchain technology that determines the validation of transactions and the minting of new blocks based on the participant’s stake in the cryptocurrency network.In contrast to proof-of-work(PoW),which relies on computational power to validate transactions,PoS employs a deterministic and resourceefficient approach to elect validators.Whereas,an inherent risk of PoS is the potential for centralization among a small cohort of network participants possessing substantial stakes,jeopardizing system decentralization and posing security threats.To mitigate centralization issues within PoS,this study introduces an incentive-aligned mechanism named decentralized proof-of-stake(DePoS),wherein the second-largest stakeholder is chosen as the final validator with a higher probability.Integrated with the verifiable random function(VRF),DePoS rewards the largest stakeholder with uncertainty,thus disincentivizing stakeholders from accumulating the largest stake.Additionally,a dynamic evolutionary game model is innovatively developed to simulate the evolution of staking pools,thus facilitating the investigation of staking pool selection dynamics and equilibrium stability across PoS and DePoS systems.The findings demonstrate that DePoS generally fosters wealth decentralization by discouraging the accumulation of significant cryptocurrency holdings.Through theoretical analysis of stakeholder predilection in staking pool selection and the simulation of the evolutionary tendency in pool scale,this research demonstrates the comparative advantage in decentralization offered by DePoS over the conventional PoS.
基金supported by the National Natural Science Foundation of China(Grant No.71872122)the Late-stage Subsidy Project of Humanities and Social Sciences of the Education Department of China(Grant No.20JHQ095).
文摘The green retrofit of existing public buildings is a necessary choice to promote energy conservation,emission reduction,and sustainable development goals in the construction industry,and to advance the implementation of the national"carbon peaking and carbon neutrality"strategy.The effective governance of green retrofit projects for existing public buildings essentially involves a dynamic process of repeated strategic interactions among key stakeholders.From the perspective of project governance,this study clarifies the game-theoretic relationship between ESCO and owners under government guidance,and constructs an evolutionary game model involving the government,ESCO,and owners.The study explores the strategic choices of the core stakeholders in the green retrofit projects of existing public buildings.The aim is to lay a foundation for research on the decision-making coordination and implementation mechanisms between ESCO and owners,thus promoting the efficient and healthy development of green retrofit projects for existing public buildings.
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This work was partially supported by National Natural Science Foundation of China （Nos. 61273013, 61333001, 61104065, 61322307）.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.71871171,71871173,and 71832010)
文摘One of the assumptions of previous research in evolutionary game dynamics is that individuals use only one rule to update their strategy. In reality, an individual's strategy update rules may change with the environment, and it is possible for an individual to use two or more rules to update their strategy. We consider the case where an individual updates strategies based on the Moran and imitation processes, and establish mixed stochastic evolutionary game dynamics by combining both processes. Our aim is to study how individuals change strategies based on two update rules and how this affects evolutionary game dynamics. We obtain an analytic expression and properties of the fixation probability and fixation times(the unconditional fixation time or conditional average fixation time) associated with our proposed process. We find unexpected results. The fixation probability within the proposed model is independent of the probabilities that the individual adopts the imitation rule update strategy. This implies that the fixation probability within the proposed model is equal to that from the Moran and imitation processes. The one-third rule holds in the proposed mixed model. However, under weak selection, the fixation times are different from those of the Moran and imitation processes because it is connected with the probability that individuals adopt an imitation update rule. Numerical examples are presented to illustrate the relationships between fixation times and the probability that an individual adopts the imitation update rule, as well as between fixation times and selection intensity. From the simulated analysis, we find that the fixation time for a mixed process is greater than that of the Moran process, but is less than that of the imitation process. Moreover, the fixation times for a cooperator in the proposed process increase as the probability of adopting an imitation update increases; however, the relationship becomes more complex than a linear relationship.
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 Natural Science Foundation of China(61503225)the Natural Science Foundation of Shandong Province(ZR2015FQ003,ZR201709260273)
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 71231007, 71071119, and 60574071
文摘Traditional evolutionary games assume uniform interaction rate, which means that the rate at which individuals meet and interact is independent of their strategies. But in some systems, especially biological systems, the players interact with each other discriminately. Taylor and Nowak (2006) were the first to establish the corresponding non-uniform interaction rate model by allowing the interaction rates to depend on strategies. Their model is based on replicator dynamics which assumes an infinite size population. But in reality, the number of individuals in the population is always finite, and there will be some random interference in the individuals' strategy selection process. Therefore, it is more practical to establish the corresponding stochastic evolutionary model in finite populations. In fact, the analysis of evolutionary games in a finite size population is more difficult. Just as Taylor and Nowak said in the outlook section of their paper, 'The analysis of non-uniform interaction rates should be extended to stochastic game dynamics of finite populations.' In this paper, we are exactly doing this work. We extend Taylor and Nowak's model from infinite to finite case, especially focusing on the influence of non-uniform connection characteristics on the evolutionary stable state of the system. We model the strategy evolutionary process of the population by a continuous ergodic Markov process. Based on the limit distribution of the process, we can give the evolutionary stable state of the system. We make a complete classification of the symmetric 2×2 games. For each case game, the corresponding limit distribution of the Markov-based process is given when noise intensity is small enough. In contrast with most literatures in evolutionary games using the simulation method, all our results obtained are analytical. Especially, in the dominant-case game, coexistence of the two strategies may become evolutionary stable states in our model. This result can be used to explain the emergence of cooperation in the Prisoner is Dilemma Games to some extent. Some specific examples are given to illustrate our results.
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 National Natural Science Foundation of China(71571082,71471073)the Fundamental Research Funds for the Central Universities(CCNU14Z02016,CCNU15A02046)
文摘Personalized products and services in e-commerce bring consumers many new experiences, but also trigger a series of information security issues. Considering the bounded rationality of the game participants, in this paper, we propose an evolutionary game model of privacy protection between firms and consumers based on e-commerce personalization. Evolutionary stable strategies（ESSs） are obtained from the equilibrium points according to the model analysis, and then simulation experiments are launched to validate the decision-making results and the influencing mechanism of various factors. The results show that the model can eventually evolve toward a win-win situation by wisely varying its various factors, such as ratios of initial strategies, cost of privacy protection, commodity prices, and other related factors. Further, we find that reducing the possibility of the privacy breach under the premise of privacy protection can help promote the e-commerce personalization.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 71071119 and 60574071
文摘Evolutionary game dynamics in finite size populations can be described by a fitness-dependent Wright- Fisher process. We consider symmetric 2×2 games in a well-mixed population. In our model, two parameters to describe the level of player＇s rationality and noise intensity in environment are introduced. In contrast with the fixation probability method that used in a noiseless case, the introducing of the noise intensity parameter makes the process an ergodic Markov process and based on the limit distribution of the process, we can analysis the evolutionary stable strategy （ESS） of the games. We illustrate the effects of the two parameters on the ESS of games using the Prisoner＇s dilemma games （PDG） and the snowdrift games （SG）. We also compare the ESS of our model with that of the replicator dynamics in infinite size populations. The results are determined by simulation experiments.
基金supported partly by National Natural Science Foundation of China(Nos.61074114 and 61273013)
文摘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.
基金supported by the Innovation Foundation of Shanghai Municipal Education Commission (Grant No.09YS47)
文摘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.
基金supported by the National Key R&D Program of China(2017YFB1400105).
文摘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.
基金The National Natural Science Foundation of China(No.51577028).
文摘In order to protect the interests of electric vehicle users and grid companies with vehicle-to-grid(V2G)technology,a reasonable electric vehicle discharge electricity price is established through the evolutionary game model.A game model of power grid companies and electric vehicle users based on the evolutionary game theory is established to balance the revenue of both players in the game.By studying the dynamic evolution process of both sides of the game,the range of discharge price that satisfies the interests of both sides is obtained.The results are compared with those obtained by the static Bayesian game.The results show that the discharge price which can benefit both sides of the game exists in a specific range.According to the setting of the example,the reasonable discharge electricity price is 1.1060 to 1.4811 yuan/(kW·h).Only within this range can the power grid company and electric vehicle users achieve positive interactions.In addition,the evolutionary game model is easier to balance the interests of the two players than the static Bayesian game.
基金supported by the National Natural Science Foundation of China(61872006)Scientific Research Activities Foundation of Academic and Technical Leaders and Reserve Candidates in Anhui Province(2020H233)+2 种基金Top-notch Discipline(specialty)Talents Foundation in Colleges and Universities of Anhui Province(gxbj2020057)the Startup Foundation for Introducing Talent of NUISTby Institutional Fund Projects from Ministry of Education and Deanship of Scientific Research(DSR),King Abdulaziz University(KAU),Jeddah,Saudi Arabia(IFPDP-216-22)。
文摘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.
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supported by the National Natural Science Foundation of China(71901217)the Key Primary Research Project of Primary Strengthening Program(2020-JCJQ-ZD-007).
文摘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.
基金The National Natural Science Foundation of China(No.61741102,61471164)
文摘To satisfy mobile terminals ’( MTs) offloading requirements and reduce MTs’ cost,a joint cloud and wireless resource allocation scheme based on the evolutionary game( JRA-EG) is proposed for overlapping heterogeneous networks in mobile edge computing environments. MTs that have tasks offloading requirements in the same service area form a population. MTs in one population acquire different wireless and computation resources by selecting different service providers( SPs). An evolutionary game is formulated to model the SP selection and resource allocation of the MTs. The cost function of the game consists of energy consumption,time delay and monetary cost. The solutions of evolutionary equilibrium( EE) include the centralized algorithm based on replicator dynamics and the distributed algorithm based on Q-learning.Simulation results show that both algorithms can converge to the EE rapidly. The differences between them are the convergence speed and trajectory stability. Compared with the existing schemes,the JRA-EG scheme can save more energy and have a smaller time delay when the data size becomes larger. The proposed scheme can schedule the wireless and computation resources reasonably so that the offloading cost is reduced efficiently.
