Explaining the evolution of cooperation remains one of the important problems in both biology and social science. Classical theories mainly based on an assumption that cooperative players are symmetrically interacted. However, almost all the well-studied systems showed that cooperative players are in fact asymmetrically interacted and that asymmetric interaction might greatly affect cooperation behavior of the involved players. Considering the asymmetric interaction and the selection pressure of resources, we present a model that possesses four strategies: strengthcooperation (SC), strength-defection (SD), weakness-cooperation (WC) and weakness-defection (WD). Combining evolutionary game theory with dynamical stability theory, we find that the evolutionary results closely depend on the asymmetric interaction and selection pressure of resources as well as cost-to-benefit ratio of conflict. When the common resources are plentiful, the cost-to-benefit ratio of conflict is negatively correlated with the probability of SC, while it is positively correlated with the probability of SD and WD. With increasing the strength ratio between the strong and weak players, the proportion of SC and SD will increase, while the proportion of WD will reduce. The model developed here has intrinsically integrated Boxed Pigs game and Hawk-Dove game. When the common resource is at shortage, the Boxed Pigs game will transform into Hawk-Dove game under the increase of the strength ratio between the strong and weak players.

The co鄄evolution between parasite and its host is one of the most important research field in both population ecology and biological forecasting, such as crop cultivation, livestock breeding, excessive copies of pathogenic cells, and so on. The main models for studying host鄄parasite interactions include: (1) The classical Lotka鄄Volterra model and Leslie model, which showed that the host鄄parasite system could have diversified dynamical behaviors, including local asymptotic stability, global asymptotic stability, limit cycle, bifurcation phenomenon, chaotic phenomena, and so on; (2) Epidemic models, which are developed to explain whether the spread of virus will depend on the threshold value. If the amount of virus is higher than the threshold value, infectious will be maintained, whist the infectious will tend to disappear, if the amount of virus is lower than the threshold value; (3) The Nicholson鄄Bailey model with discrete time variable. The model demonstrates that host and parasite population system might form a coupling vibration. The oscillation in this model is not stable, and any disturbance might lead to non鄄equilibrium of the system. The improved models will display more diversified dynamical behaviors such as Hopf bifurcation, period鄄doubling bifurcation, chaotic phenomenon, etc. All above鄄mentioned models for co鄄evolution between hosts and parasites are based on an assumption that the increase