We design a lightweight Overlay Network, called Arigatoni, that is suitable to deploy the Global Computing Paradigm over the Internet. Communications over the behavioral units of the model are performed by a simple communication protocol. Basic Global Computers can communicate by first registering to a brokering service and then by mutually asking and offering services, in a way that is reminiscent to Rapoport's "tit-for-tat" strategy of cooperation based on reciprocity. In the model, resources are encapsulated in the administrative domain in which they reside, and requests for resources located in another administrative domain traverse a broker-2-broker negotiation using classical PKI mechanisms. The model is suitable to fit with various global scenarios from classical P2P applications, like file sharing, or band-sharing, to more sophisticated Grid applications, like remote and distributed big (and small) computations, to possible, futuristic real migrating computations. Indeed, our model fits some of the objectives suggested by the CoreGrid Network of Excellence, as described in Schwiegelshohn et al. (Schwiegelshohn et al., 2005).