In this paper we consider the problem of maximising utility in linked market-driven distributed and Grid systems. In such systems, users submit jobs through brokers who can virtualise and make available the resources of multiple service providers, achieving greater economies of scale, improving throughput and potentially reducing cost. Customers compete against each other by assigning a utility value or function to the successful processing of their jobs in an effort to have them prioritised in the face of contested and constrained resources. Brokers and service providers also attempt to maximise the utility they gain, choosing to process jobs that will earn them the highest profit with respect to the resources required. For this to be effective over many linked computing marketplaces highly distributed resource allocation is needed, where each participant can operate independently using only local information, and ideally reach a global state where all participants are satisfied. W...