The Evolution Of Cooperation In Social Dilemma Game

Cooperation exists widely in nature and human society.However,cooperation means that individuals need to sacrifice their own interests and selfish individuals exploit the interests of cooperators through betrayal to obtain higher interests,which will be disadvantageous for cooperators in the process of natural selection.Understanding the emergence of cooperation has become a problem that perplexes many scientists.For the traditional classic non-cooperative game theory,fully rational individuals will choose defection that strict dominant strategy,and cooperation will not possibly exist.The theory assumes that the participants are completely rational and each participant makes decisions based on the principle of maximizing self-interest,which is common knowledge for all participants.Under this premise,each participant will make an accurate decision in a given game structure and game environment.However,in reality,participants have limited knowledge,imagination and computational power in a highly uncertain and extremely complex decision-making environment of the game.It is difficult for participants to have perfect prediction and decision-making ability for the game to make complete rational decision.Taking all these above factors into consideration,it is difficult for participants to make a completely rational decision.When making decisions,they often consider their past experiences,behavioral habits,and decision-making behaviors in similar situations.So people put forward the concept of bounded rationality and construct evolutionary game theory.Under the assumption of individual bounded rationality,participants will not make the completely rational optimal decision,and people constantly adjust their own strategies through continuous learning.The evolutionary game theory has made a good explanation for the emergence of cooperation in social dilemmas such as prisoner's dilemma and public goods game,and has gradually become an important theoretical tool for studying the emergence of cooperation in social dilemmas.This paper systematically introduces the theoretical knowledge about the promotion of cooperation in evolutionary games,including complex network theory,"green beard effecct" theory,voluntary participation mechanism,punishment in social dilemma and stochastic game,and reviews relative researches of cooperation in social dilemma based on the above theory.Based on the above theory,this paper has made further research on the cooperation in social dilemma,including the following four aspects:Firstly,we are inspired by the intelligent optimization algorithm and construct a strategy update rule based on particle swarm optimization algorithm in evolutionary games.Under the strategy update rule,each participant will update its strategy according to the optimal strategy through its own history and the current optimal strategy of the neighbor.We first study the evolution of cooperation in the prisoner's dilemma and the snowdrift game on regular network.The research shows that the strategy update rule can effectively promote cooperation,and even in the unfavorable situation that cooperation cost is very high,the population still maintains a certain level of cooperation.At the same time,in the snowdrift game,the update rule offsets the suppression of cooperation by the spatial structure in the case of high cooperation cost,and therefore the cooperation level of the population is higher than the mixed Nash equilibrium.Cooperators will gather under the strategy update rule in the snowdrift game as well.The lower imitation trade-off coefficient makes individuals tend to adopt either full cooperation or full defection and promote the aggregation of fully cooperative individuals.The higher imitation trade-off coefficient makes the population presents highly heterogeneous cooperation level and the fully cooperative individuals cannot gather.We further study the prisoner's dilemma on BA scale-free network when participants obtain the average payoff,and construct the particle swarm optimization strategy update rules in both continuous and mixed strategy systems.The research results show that the strategy update rule can significantly improve the level of population cooperation in the case of continuous strategy.In the case of mixed strategy,the strategy update rule will make the level of cooperation of the population decrease sharply and cause the collapse of cooperation.Nodes with low and medium degrees play an important role in the evolution of cooperation.Secondly,in the case that each individual has an identifiable label and its strategy space is consist of unconditional cooperation,unconditional defection,intra-group cooperation and inter-group cooperation,we studied the influence of the “green beard effect” on the evolution of cooperation under the strategy update rule based on particle swarm optimization.Each individual will decide whether to cooperate according to their own and their opponent's labels and strategy types.Studies have shown that lower imitation trade-off factors result in the aggregation of individuals with the same strategy type.There is no significant difference between the intra-group cooperation and the inter-group cooperation strategies when the individual has only the ability to update the strategy without the ability to reproduce.When an individual has both strategy update and reproduction ability,the introduction of individual reproductive ability under the small imitation trade-off coefficient and cooperation cost enables the intra-group cooperation to quickly occupy the entire population.The higher the migration ability of individual offspring,the more favorable the maintenance of inter-group cooperation in the population.Thirdly,we study the evolution of cooperation in the public goods game when cooperators evenly share the cost of punishment.In this model,cooperators will not only contribute to the public good but also pay a cost that will be equally shared by the cooperators to punish free riders.We first study the evolution of cooperation under infinite populations.Study results have shown that the introduction of this punishment is conducive to the evolution of cooperation and promote cooperation as the only evolutionary stable equilibrium.Then,we study the finite population on the regular network.The research results show that the introduction of the network structure causes the cooperation to survive in the population under the smaller penalty threshold.In this case,the internal equilibrium point that cooperation and defection coexist becomes evolutionary stable equilibrium.However,when the fine is large,cooperation will have a larger basin of attraction in the well-mixed population than that in the structured population.The joint effect of networks and punishment will not always promote cooperation.Finally,we introduce a voluntary participation mechanism.Research shows that the introduction of non-participation strategy makes defection no longer become an evolutionary stability strategy.The introduction of this strategy makes cooperation become only evolutionary stable strategy under the lower penalty threshold.The introduction of non-participation strategies does have a role in promoting cooperation to a certain extent.Finally,we study the evolution of cooperation in both stochastic prisoner's dilemma and stochastic public goods game.Previous studies usually assume that the return matrix of the game is fixed,and in reality,the payoff matrix of the game will vary depending on the historical actions of both parties.Therefore,we establish a stochastic prisoner's dilemma and stochastic public goods game model based on the stochastic state transition of payoff matrix on the regular network structure.The results show that in the stochastic prisoner's dilemma game,when the difference in the return between the two game states is less than the cooperation cost,the stochastic change of the game state will reduce the cooperation level of the population.The more stringent the condition that the game state shifts to the high-yield game state,the more unfavorable the cooperation.When the difference in the return between the two game states is greater than the cooperation cost,the stochastic change of the game state will promote the cooperation level of the population.The Always coopeartion(ALLC)and “tit-for-tat”(TFT)strategies are more advantageous than the “win-stay lose-shift”(WSLS)strategy.In the stochastic public goods game,stochastic changes in the game state will also reduce the cooperation level of the population.The more severe the condition that the game state shifts to the high-yield game state,the more unfavorable the maintenance of cooperation in the population,which even leads to the collapse of cooperation.In the stochastic public goods game,the “win-stay lose-shift”(WSLS)strategy has obvious advantages for the maintenance of population cooperation.