Spatial games and the maintenance of cooperation in an asymmetric Hawk-Dove game

Classical theories explaining the evolution of cooperation often rely on the assumption that the involved players are symmetrically interacted. However, in reality almost all well-documented cooperation systems show that cooperative players are in fact asymmetrically interacted and that this dynamic may greatly affect the cooperative behavior of the involved players. Here, we developed several models based on the most well known spatial game of the Hawk-Dove game, while also considering the effects of asymmetric interaction. Such asymmetric games possess four kinds of strategies: cooperation or defection of strong player and cooperation or defection of weak player. Computer simulations showed that the probability of defection of the strong player decreases with decreasing the benefit to cost ratio, and that all kinds of strategy will be substituted by cooperation on behalf of the strong player if the benefit to cost ratio is sufficiently small. Moreover, weak players find it difficult to survive and the surviving weak players are mostly defectors, similar to the Boxed Pigs game. Interestingly, the patterns of kinds of strategies are chaotic or oscillate in some conditions with the related factors.