The Evolution Of Cooperation In Asymmetric Cooperative Systems

Evolution of cooperation behavior and cooperative stability are key issues affecting the evolution of life itself. Sociologists, economist and biologist have all spent great research efforts in trying to disentangle their principles. Depending on the resulting benefits, single individuals and species are bound together by dualis-tic relationships based at times by cooperation and at times by competition. What remain to be fully explain in evolution of cooperation is the factors involved in inhibiting competition in favor of the maintenance of cooperation. Classical the-ories of Kin selection and Reciprocity selection have suggested that self-restraint or spatial heterogeneity (restraint) will prevent direct conflict between the players resulting in the stability of cooperative systems. Recently, however, an increasing number of studies have found that genetic similarity or mutual reciprocity alone are not sufficient to justify the stability of cooperation. These theories in fact encounter significant problems in relation to cheating. They in fact give little cues on why and how some individuals turn their strategy into non-cooperation to the extent of becoming cheaters.The main models used for modeling the evolution of cooperation, including Hamilton’s rule, Iterated Prisoners’Dilemma, and group selection, are essentially based on the assumption that cooperative player are bound by mathematically symmetric interactions. However, the empirical data/observations have shown that there exist asymmetric interactions within cooperative interactions. In this dissertation, we create some evolutionary dynamic games which incorporate the asymmetric element. We also discuss the issues that the players are involved in when choosing different strategies and the stability of cooperation system can be effectively maintained.Firstly, we study the passive selection in the form of reward and punishment produced by asymmetric interaction. We propose a collective punishment/reward mechanism, and incorporate it into a multiplayer snowdrift game. Our model demonstrates that collective punishment is more effective than collective reward for promoting cooperation. At the same time, the stability of mutualisms can be maintained by the use of collective punishment and collective reward mecha-nisms. These results show that passive selection might be one of the most impor- tant dynamics in the evolution of cooperation. These results have the potential to explain why dominant individuals prefer punishing less cooperative behavior finally increasing the stability of cooperative systems. In addition, obtaining our results from a multiplayer snowdrift game with intro-specific and inter-specific interactions, we show that the intra-specific interaction can maintain the stability of mutualism when the mutualistic systems do not consider other mechanism, as well as it can result in multi-equilibriums. Not only can these results explain the stability of mutualism, but also provide the theoretical basis justifying previous experimental results which found that competition avoids the tragedy of commons in the fig and fig wasp system.Secondly, incorporating the asymmetry in the strategy sets, we construct an asymmetric game model with the so-called carrot-stick strategy, which is a mixed strategy of reward and punishment. Based on numerous mathematical analyses, it is unveiled that this asymmetric interaction can lessen the dilemma of coop-eration:the dominant players and recipient players might coexist through cycle frequency. Further analysis shows that several equilibrium statuses are possi-ble, and they depend on the payoff parameters and the initial conditions. These theoretical observations are consistent with existing empirical evidence that asym-metric sanction or reward of host species are at the base of the conflicts between fig tree and fig wasps or in between cleaner fish and-clients mutualisms. Fur-thermore, we study the effect of environmental selection pressures and the benefit to cost ratio in spatial games by using the asymmetric evolutionary game. Our simulations show that cooperative equilibrium can occur under relative small en-vironmental selection pressures; meanwhile the cooperation interaction between the cooperative actors and recipient varies chaotically and oscillate with a certain frequency.Thirdly, we study how the resulting benefits will be allotted to the partic-ipants when cooperation is maintained. The model we propose shows that the allocations for a common benefit vary when the effect of a reward mechanism is included in the model. The outcome is a shift from the well-known Red Queen effect to the Red King effect and vice versa. In addition, our model shows that either an asymmetry in payoff or an asymmetry in the number of cooperative partners causes a shift between the Red Queen effect and the Red King effect.The results of this dissertation provide some useful foundations for the ori- gin and evolution of cooperation, and the maintenance and management of the ecosystem. Furthermore, such research might provide theoretical guidance and inspiration for epidemic prevention and prediction, for the pollination or nitro-gen fixation of plants in agricultural production and for other practical subjects directly related to the sustainable development of human societies.