Evolutionary Game Model Improvement And Its Applications

Evolutionary game theory is a subject that is used to study how to balance the decisions.Due to its assumption of imperfect rationality, more and more scholars have taken considerable interest, and it has been widely used in various fields. However, its research mostly has remained in the traditional evolutionary game system, which exist some deficiencies. According to this, the study in this paper is carried out.On the one hand, for the origin of traditional evolutionary system, the concept of strength coefficients is obtained with rationality in the derivation process, which reflects the interdependence of different game participants in the decision making. Through the relevant knowledge of the ordinary differential equations theory and dynamics theory, compared with the original evolutionary game system, the study shows that if the ratio of strength coefficient for two decisions is the same, so the stable-state decisions don’t change, instead, if this ratio is greater than one,so the former decision stable state will be better in the game group and will be imitated.On the other hand, considering the inevitable disruption of random factors for the bounded rational game participants in the game, combing the natural characteristics of species interaction and species mutual promotion, based on the game system with strength coefficient, random items with the Gauss white noise are added. In addition, owing to Markov of this model system, through the stochastic differential equations theory and the statistical dynamics theory,the study shows that game participants are not affected by random factors as not to change their decision-making within a certain range, and even if affected, but if the number of game group is smaller, so the impact will be smaller. Besides, the final decision of steady state will be the same after a long enough game time.Finally, as to the recent topic of free public toilets paper supply, from the point view of evolutionary game theory, the decision-making issues are analyzed between the toilets management department and the citizens, the validity of the modified model is once again demonstrated, and some reasonable suggestions between the toilets management department and the citizens are separately proposed according to the research results.The detailed structure of this paper is shown as follows:The first chapter describes the selecting background and research significance. And according to research situation of the domestic and foreign about the evolutionary game in recent years, the work of this paper is presented through the summary.The second chapter briefly describes the related concepts of game theory, like its definition, its classification as well as Nash equilibrium. And two basic concepts of the evolutionary game, namely, evolutionary stable strategy and the replicator dynamics equation are introduced, and the connection between evolutionary stable strategy and Nash equilibrium is discussed.The third chapter firstly derives the game system with strength coefficients, which is the improvement of the original evolutionary game system. Secondly, some relevant properties of this system solution are studied, such as existence, uniqueness as well as stability. Finally, the impact of strength coefficients on game steady-state decision is again illustrated by using the Maple 7 simulation.Based on the third chapter analysis, the fourth chapter establishes game system with random items. Similarly, the existence and uniqueness of the system solution are first studied, as well as its mean square exponential stability. Secondly, because of the characteristics of Markov for system solution, probability density distribution of the system solution is studied, and then the mean, variance and game system equilibrium phase change are further discussed. Finally, the effects of random factors on decision-making are again comparative studied through the explicit forward Euler numerical method.In the next chapter, that is, the fifth chapter, for the current social focus topic of free toilet paper provide, based on the game model modified in this paper, game strategies between the toilets management department and the citizens are analyzed. In addition, according to the model results, some appropriate and reasonable suggestions are put forward.As a whole, the sixth chapter summarizes the research results and proposes further possible research.