The Evolution Of Cooperation In Asymmetric Systems

The cooperation behaviors exist in almost life systems including human society, but explaining the evolution of cooperation remains one of the greatest problems for both biology and social science. Adam Smith and Darwin had tried to make clear this problems via hypothesizes of rational man and individual adaption; however, these theories were confronted with the difficulty of explaining why altruism behaviors exist in life systems. Hamilton and Trivers suggest that cooperation between partners can be maintained through genetic similarity or reciprocity relatedness. However, the researches of Boyd&Lorberbaum and Hauert&Doebeli show that the mechanism of kin and reciprocity selection might not be credible for maintaining a stable cooperation interaction.These classical theories are based on an assumption that partners interact symmetrically with equal payoffs in a game of cooperation interaction. Whereas in fact, cooperative partners are in an asymmetric interaction which has been empirically implied in many real cooperation systems. The assumption of symmetry might be what raises the dilemma of these classic theories of the evolution of cooperation. In this dissertation, we present some mathematical models based on asymmetric interaction to analyses the evolution of cooperation.Firstly, we find that the asymmetric relationship is one of the key dynamics of the evolution of cooperation based on Hawk—Dove model with asymmetric interaction. Combing asymmetry and relatedness in volunteer's dilemma game, it shows that the probability of volunteerism in such systems depends closely on both the degree of asymmetry and level of relatedness between interacting individuals. In the presence of asymmetrical interactions, subordinate players were more likely to offer public goods than the dominant player. More asymmetrical interactions decrease the probability of volunteerism of the dominant player; overall volunteerism increases with increasing relatedness. Based on the volunteer's dilemma game with the super-rationality and asymmetric interaction, it shows that the strong player was more likely to offer public good than weak players in an asymmetric cooperation system when the group size is larger than the critical point. The integration of super-rationality and asymmetric interaction might have the potential to explain why different kind of individual would like to provide the common goods in the cooperation systems ranging from the less coherent systems to eu-society.Secondly, we analyze the evolutionarily stable strategy of asymmetric systems through the replicator dynamic. Based on the asymmetric volunteer's dilemma game, we find two evolutionary stable strategies in cooperation system that suggests whether the strong or weak players produce a public good closely depends on the initial condition of individual strategies. These results enrich Selten's demonstration that public goods can only be produced by a strong player. Based on the cost-benefit theory which links dynamic game theory overpass the battle of the sexes game to analysis the evolution of the mating systems, it suggests that the mating systems might be a continuum with flexibility for the changing environment.Thirdly, we study the effect of asymmetric interaction and the benefit to cost ratio in spatial games by using the asymmetric Hawk-Dove game. Our simulations show that increasing the cost of defection will increase the probability of cooperation, meanwhile the cooperation interaction between the cooperative actors and recipient is chaotically vary or oscillate with the change of related factors. Such reseaches in this dissertation might provide a theoretical explanation for cooperation stability of the social organizations of human, also, it may be give some inspirations for investigation of the market behavior, ecological protection or other fields.