Resource allocation is one of the principal stages of query processing in relational data grid systems. Specific characteristics of the data grid environment, such as dynamicity, heterogeneity and large scale, impose serious restrictions to the resource allocation process. Static resource allocation before the query execution may be far from optimal due to the dynamic changes of the system. One possible optimization is to adjust dynamically the allocation of resources during the query execution. Some methods of dynamic resource allocation have been proposed, however, most of them use centralized control mechanisms. In this study we argue that the decentralized approach meets better the requirements of the data grid systems. In this study we propose a decentralized method of dynamic resource allocation that is based on the mobile agent paradigm. We consider the participating nodes as autonomous and independent elements of the system, each of which can detect if it is overloaded and make the decision to react. Then we consider each relational operation as a mobile agent running on the allocated node, meaning that, it keeps track of its own status and can migrate to another node at any time. A two-level cooperation mechanism between such autonomous nodes and autonomous operations is described in detail. Performance evaluation proves the efficiency of the proposed method.