Dynamics In The Self-organized Division Of Labor Based On Evolutionary Game Theory

Early division of labor models were mainly inspired by clustering behavior of social insect and animal,most of which belonged to exploratory models,aiming to reveal the law and nature of changes of individual's state in a given hypothesis.With the development of evolutionary game theory,its application can be extended to the research field of task allocation.The framework describing the evolution of population strategy can be used to abstractly model the phenomenon of task allocation and explain the emergence of division of labor and cooperation in populations with the help of evolutionary game theory.Individuals in a population can achieve the effect of division of labor and cooperation at the population level by performing specific tasks,which can be regarded as a special form of cooperation.However,due to the self-interest nature of individuals,they tend to choose tasks with higher payoffs in order to improve their own interest level,but the dominance of a single strategy will undoubtedly hurt the interests of the population,resulting in the division of labor and cooperation dilemma.This paper takes the phenomenon of task allocation as a breakthrough point to study how low-payoff task survives in a population of selfish individuals.Specific research is carried out from the following aspects:(1)The replicator dynamics of evolutionary game theory is used to analyze the division of labor game model with lazy individuals.Considering the complex network structure in real society,the model is further applied to BA scale-free network and lattice network.The results of theoretical analysis and simulation experiments show that the task allocation depends on the cost and benefit of the task and the interaction structure between the game players.(2)Considering the limitations of replicator dynamics in choosing candidate strategies when updating strategies and the influence of different social roles on task allocation,the division of labor game model with destroyers is theoretically analyzed by means of improved Smith dynamics.According to the parameters in the payoff matrix,there are four specific scenarios.For each case,the corresponding equilibrium points are calculated and the stability is judged.(3)The number of individuals in the real population is limited.Considering the influence of randomness on the evolutionary results,this paper studies the strategy evolution of division of labor game model in the finite population.Fixation probabilities of two-player and multi-player two-strategy division of labor game model with arbitrary selection intensity are derived,and the effects of relevant parameters on fixation probabilities are explored.Furthermore,the fixation probability and fixation time of two-player division of labor game model under weak selection are obtained,and a comparison with neutral selection is performed.In addition,the accuracy of the theoretical results is verified by simulation experiments.