Sensor networks are large scale networks consisting of several nodes and some base stations. The nodes are monitoring the environment and send their measurement data towards the base stations possibly via multiple hops. Since the nodes are often battery powered, an important design criterion for sensor networks is the maximization of their lifetime. In this paper, we consider multi-domain sensor networks, by which we mean a set of sensor networks that co-exist at the same physical location but run by different authorities. In this setting, the lifetime of all networks can be increased if the nodes cooperate and also forward packets originating from foreign domains. There is a risk, however, that a selfish network takes advantage of the cooperativeness of the other networks and exploits them. We study this problem in a game theoretic setting, and show that, in most cases, there is a Nash equilibrium in the system, in which at least one of the strategies is cooperative, even without introducing any external incentives (e.g., payments).