Stochastic Evolutionary Dynamics Of Cooperation And Competition Among Individuals

Evolutionary game theory has been an important method of studying the behavior ofcooperation and competition among individuals, since it was proposed by John Maynard andGeorge Price and developed by a remarkable number of scholars. The Hawk-Dove game is widelyused to study the ubiquitous phenomena of competition and conflict in human society and theanimal world, in which the Hawk strategy means competition while the Dove strategy meanscooperation. The snowdrift game is often used in the research of cooperation behavior amongindividuals. However, the behavior of cooperation and competition in the real world is subject tovarious factors, and presents tremendous flexibility. So it is necessary to develop more reasonablegame models and further to study the behavior of cooperation and competition among individuals.In this paper, we generalize the Hawk-Dove game in two different aspects. Firstly, the(two-player) Hawk-Dove game is generalized to the multi-player game. Secondly, a maximumdemand limit is introduced into the traditional Hawk-Dove game. We then build two new gamemodels. The evolutionary game dynamics of cooperation and competition in both infinite andfinite populations are discussed and the effects of all parameters on the evolutionary gamedynamics are analyzed based on the new models. Moreover, we also study the Snowdrift gamewith the personality trait mechanisms. We assume that the population consists of generous andselfish individuals. The generous individuals tend to cooperate while the selfish individuals tend todefect. Individuals obtain a negative psychological benefit when they take the strategies thatviolate their personality traits. Under this new mechanism, we analyze the system stability and thestable proportion of cooperators through analyzing the replicator equations.