Research On The Influence Of Mixed Update Rules And Exit Option On Cooperative Behavior

Cooperative behavior is widespread in the survival and reproduction of various species,and it is also the basis for the development of human civilization.At present,“how does cooperative behavior develop”has become a problem that scientists in many fields concentrate on.Based on the framework of evolutionary game theory,we adopt methods,such as,random processes and replication dynamic equations,to study the relevant mechanisms that affect the evolution of cooperation in the population in this paper.First,we investigate the evolutionary games that combined the imitation update rule and the average payoff-driven update rule in finite populations,in which both one-shot and iterated prisoner's dilemma game with positive assortment are implemented.The average abundance of cooperators is obtained through the transition probabilities and the properties of Markov chain.Both numerical and analytical results show that the effectiveness of the average payoff-driven update rule for the promotion of cooperation depends on whether there is a reciprocity mechanism in the system.In detail,average payoff-driven update rule is better than imitation update rule only when our model has one of the following three conditions:(1)small probability of the positive assortment;(2)small probability to the next round;(3)small probability of knowing one's reputation.If the above conditions are not satisfied,then imitation update rule is most effective for the promotion of cooperation.We thus provide a deeper understanding for the effectiveness of these rules regarding the promotion of cooperation.Secondly,we consider a pairwise game with conditional exit strategies in infinite population.Through establishing the replication dynamic equations,we study the evolutionary game dynamics of the population,as well as obtain the conditions of system stability in prisoner's dilemma game,snowdrift game,stag hunt game and harmony game.According to numerical simulations,it is found that the impact of the benefit and cost of exit on the evolution of cooperation depends on the type of the game.In detail,cooperation can be promoted effectively when the benefits of exiting in prisoner's dilemma game and stag hunt game are greater than the exit cost under the condition of only cooperators having the right to exit.Instead,if only defectors can exit,cooperators are favored only if the benefits of exiting the game in snowdrift game and coordination game are less than the exit cost.In other cases,the benefits and costs of exiting the game have little effect on the evolution of cooperation in the population.These results are conducive to encourage the development of cooperation in the population with exit options.The result obtained in this paper are a supplement and improvement to the evolutionary game theory.It also provides a new perspective for researches on cooperative behavior in populations.The evolutionary dynamics of populations is carried out through a reasonable combination of statistics,economics,sociology,mathematics and other disciplines.The research is helpful to understand the generation and development of cooperative behavior,and find an effective method of solving social dilemmas.