The recently deployed 4G access technology promises to satisfy the increasing demand of bandwidth consuming applications by providing high network capacity, low latency and seamless mobility. Towards this direction, concept solutions concerning the integration of wireless and optical networks have been proposed. However, the majority of these approaches assume the conventional fixed commitment of resources to the base stations, an inefficient and costly process, especially in case the Passive Optical Network (PON) belongs to a different operator. As a result, new, more dynamic backhaul resource allocation approaches are required. In this paper, the authors study the problem of committing resources of the backhaul network to a base station by employing evolutionary game theory in order to model the interactions between the subscribers and the base station. The asymptotic stability of the proposed scheme is proven under the replicator dynamics model. Finally, the impact of time delay in the proposed scheme is also investigated.