We design a lightweight communication model, called Arigatoni, with related architecture, that is suitable to deploy the Global Computing Paradig} over the Internet. Communication over the behavioral units of the model are performed by a simple communication protocol on top of TCP or UDP 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 co-operation based on reciprocity. In the model, resources are encapsulated in the intranet in which they reside, and requests for resources located in another intranet traverse a broker-2-broker negotiation using classical PKI mechanisms. The model is suitable to fit with various global scenarios from classical PtP application, like file sharing, or band-sharing, to more sophisticated GRID application, like remote and distributed big (and small) computations, until possible, futuristic real migration computations, in the vein of the programming language Obliq by Luca Cardelli.