While most game theoretical models assume that individuals randomly interact with all other group members, strong evidence indicates that individuals tend to preferentially interact with some of them. The position of an individual in a network affects, among other factors related to survival, its predation risk and competitive success. Here I then modified the Hawk-Dove game to explore the effect of social network structure on competitive strategy of individuals that differ in their fighting ability and may adjust their use of the Hawk, Dove and Assessor tactics to maximize their foraging success when they meet opponents they are connected with. From randomly generated networks, I demonstrate that phenotypic assortment by fighting ability reduces individuals' aggressiveness and, as such, favours cooperative interactions. Furthermore, the success of individuals with the weakest fighting ability is usually highest within networks where they most frequently meet opponents with the same fighting ability as their own, suggesting they might benefit from breaking connections with strong contestants. This might be the case when strong contestants systematically rely on the aggressive Hawk tactic or the risk of being predated is low and independent of the number of neighbours. Thus, I extended the model and built a dynamic model to allow individuals not only to adjust their behaviour to local conditions but also to modify the structure of the social network. The number of connections and degree of phenotypic assortment are then affected by ecological factors (e.g. resources value and predation risk), but above all by whether individuals can reliably assess the competitive ability of their opponents and adjust their behaviour accordingly. These findings provide strong evidence that behaviour can play a key role in shaping network structure and highlight the importance of considering the coevolution of network and behaviour to apprehend its consequences on population dynamics.