The increasing demand for efficient content distribution using the Internet has fuelled the deployment of varied techniques such as peer-to-peer overlays, content distribution networks and distributed caching systems. These have had considerable impact on ISP infrastructure demand, motivating the development of protocols that enable mutually beneficial cooperative outcomes.In this paper we propose a parameterised cooperation utility that can be used to study the tradeoff between the benefit that an overlay obtains from the ISPs that carry its traffic and the costs that it imposes on them. With this utility, we find a closed-form expression for the optimal resource allocation given a particular cooperation tradeoff, subject to both minimal benefit and maximal cost constraints. Since the model is implementation-independent and has very modest computational demands, it is ideal for large scale simulation. We explore the properties of the proposed model through simulation in both a simple illustrative scenario and a more complete one based on network datasets. The results obtained from the model are shown to be consistent with those of measurement-based studies of overlay-ISP collaboration.