The Evolutionary Models And Simulation For The Reciprocate Altruistic Behavior

The altruistic behavior exists widely in the evolutionary process of the population of the animal and humanity. It is an important factor in the population growth and keeping the stability of the society. We are interested in that many problems in the welfare economics can be explained with the altruistic behavior which is well studied in psychology, sociology, philosophy, administration and economics.Altruistic behavior is a kind of typical behavior of limited rationality. The evolutionary rule and the survival conditions of the altruistic behavior have been studied, and the competition and coexistence in the evolutionary process of the reciprocal altruist and selfish behavior has been analyzed. It is meaningful for the study of Behavioral Economics and Behavior Science, and for the building of the mechanism of the harmonious society.The payoff in the evolutionary games is defined as fitness (the increasing rate of population) of the population with the opinion of the economist in the studying to the population evolution. The evolution of the population behavior has been looked upon as the change of the subject's number in the process for suiting the environment. As the subject's behavior changes along with the different problems and environment, the problem is fixed in the games, the behavior is influenced by the environment only, the subject's number is a measurable, continuous and differentiable function of time in the continuous models.The main creative results are as following:The mathematical expressions of the utility function and althuistic coefficient with limited rationality are structuralized and the harmonious solution is studied in a kind of gemes replacing the payoff in tranditional games with the utility function of limited rationality.The evolutionary model for altruistic behavior is set up based on the S.& W. model.. A sufficient and necessary condition for the survival of altruistic behavior is given. The evolutionary simulation of the altruistic herd behavior verifies the convergence.The infinitely repeated game for altruistic behavior is instructed with altruistic behavior coeffient and the conclusion is proved that the social efficacy with a punishment mechanism can be achieved. And the equilibriums of the evolutionary dynamics of the altruistic behavior and selfish behavior are proved in the Fictitious Play and Best Response Dynamics.. The althuisitc coefficient as an endogenous parameter is convergent with the convergence of the evolutionary games.The competition and coexistence models of altruistic and selfish are built under some hypothesis for existing environment: if the environment has capacity restriction or not; if the selfish agent can survive alone or not. Some results are studied using the stability analysis and simulation that the society is stable if the altruistic capacity of the altruistic is stronger or the selfish capacity of the selfish is weaker, the society consisted by a single kind of population isn't stable and the society system is periodic or structural stable when it hasn't the survival restriction or the bearing capacity of the environment is growing as the population increasing.The models and conclusions are helpful to analyze the economic behavior and the mechanism of the harmony.