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Grid computing supports workload execution on computing resources that are shared across a set of collaborative organizations. At the core of workload management for grid computing is a software component, called meta-scheduler or grid resource broker, that provides a virtual layer on top of heterogeneous grid middleware, schedulers, and resources. Meta-schedulers typically enable end-users and applications to compete over distributed shared resources through the use of one or more instances of the same meta-scheduler, in a centralized or distributed manner, respectively. We propose an approach to enabling autonomic meta-scheduling through the use of a new communication protocol that -if adopted by different meta-schedulers or by the applications using them- can improve the workload execution while avoiding potential chaos, which can be resulted from blind competition over resources. This can be made possible by allowing the meta- schedulers and/or their applications to engage in a process to negotiate their roles (e.g., consumer, provider, or both), scheduling policies, service-level agreement, etc. To show the feasibility of our approach, we developed a prototype that enables some preliminary autonomic management among three different meta-schedulers, namely, GridWay, eNANOS, andTDWB.