Evolutionary dynamics of tax-based strong altruistic reward andpunishment in a public goods game

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.

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

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

Central environmental protection inspection and carbon emission reduction: A tripartite evolutionary game model from the perspective of carbon neutrality

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.

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

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

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

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

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

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

Evolutionary games and spatial periodicity

Spatial interactions are considered an important factor influencing a variety of evolutionary processes that take place in structured populations.It still remains an open problem to fully understand evolutionary game dynamics on networks except for certain limiting scenarios such as weak selection.Here we study the evolutionary dynamics of spatial games under strong selection where strategy evolution of individuals becomes deterministic in a fashion of winners taking all.We show that the long term behavior of the evolutionary process eventually converges to a particular basin of attraction,which is either a periodic cycle or a single fixed state depending on specific initial conditions and model parameters.In particular,we find that symmetric starting configurations can induce an exceedingly long transient phase encompassing a large number of aesthetic spatial patterns including the prominent kaleidoscopic cooperation.Our finding holds for any population structure and a broad class of finite games beyond the Prisoner’s Dilemma.Our work offers insights into understanding evolutionary dynamics of spatially extended systems ubiquitous in biology and ecology.

EVOLUTIONARY GAME OF DYNAMIC KNOWLEDGE EXCHANGING IN KNOWLEDGE INTERACTION

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.

Evolutionary game dynamics of combining the Moran and imitation processes

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.

Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation

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

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

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

Evolutionary Game Dynamics in a Fitness-Dependent Wright-Fisher Process with Noise

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.

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

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

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

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

Revenue optimization strategy of V2G based on 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.

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

We study the effects of the planarity and heterogeneity of networks on evolutionary two-player symmetric games by considering four different kinds of networks, including two types of heterogeneous networks: the weighted planar stochastic lattice(a planar scale-free network) and the random uncorrelated scale-free network with the same degree distribution as the weighted planar stochastic lattice; and two types of homogeneous networks: the hexagonal lattice and the random regular network with the same degree k_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).

Joint resource allocation scheme based on evolutionary game for mobile edge computing

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.

Networked Evolutionary Model of Snow-Drift Game Based on Semi-Tensor Product

This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the networked evolutionary game is built. Secondly, combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and next converted into its evolutionary dynamic algebraic form. Thirdly, the dynamic evolution process is analyzed and the final level of cooperation is discussed. Finally, the effects of the changes in the rewarding and penalty factors on the level of cooperation in the model are studied separately, and the conclusions are verified by examples.

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

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

Evolutionary game analysis of problem processing mechanism in new collaboration

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