The concept of coupling geographically distributed (high-end) resources for solving large-scale problems is becoming increasingly popular, forming what is popularly called grid computing. The management of resources in the grid environment becomes complex as they are (geographically) distributed, heterogeneous in nature, owned by different individuals/organizations each having their own resource management policies and different access-and-cost models. In this scenario, a number of alternatives exist while creating a framework for grid resource management. In this paper, we discuss the three alternative models-hierarchical, abstract owner, and market-for grid resource management architectures. The hierarchical model exhibits the approach followed in (many) contemporary grid systems. The abstract owner model follows an order and delivery approach in job submission and result gathering. The (computational) market model captures the essentials of both hierarchical and abstract owner models and proposes the use of computational economy in the development of grid resource management systems.