One of the main challenges in Grid computing is efficient allocation of resources (CPU-hours, network bandwidth, etc.) to the tasks submitted by users. Due to the lack of centralized control and the dynamic/stochastic nature of resource availability, any successful allocation mechanism should be highly distributed and robust to the changes in the Grid environment. Moreover, it is desirable to have an allocation mechanism that does not rely on the availability of coherent global information. In this paper we study a minimalist decentralized algorithm for resource allocation in a simplified Grid-like environment that meets the above requirements. We consider a system consisting of large number of heterogenous reinforcement learning agents that share common resources for their computational needs. There is no communication between the agents: the only information that agents receive is the (expected) completion time of a job it submitted to a particular resource and which serves as a re...