Although the management of resources is essential for realizing a computational grid, providing an efficient resource allocation mechanism is a complex undertaking. Since Grid providers and consumers may be independent bodies, negotiation among them is necessary. The contribution of this paper is showing that market-driven agents (MDAs) are appropriate tools for Grid resource negotiation. MDAs are e-negotiation agents designed with the flexibility of: 1) making adjustable amounts of concession taking into account market rivalry, outside options, and time preferences and 2) relaxing bargaining terms in the face of intense pressure. A heterogeneous testbed consisting of several types of e-negotiation agents to simulate a Grid computing environment was developed. It compares the performance of MDAs against other e-negotiation agents (e.g., Kasbah) in a Grid-commerce environment. Empirical results show that MDAs generally achieve: 1) higher budget efficiencies in many market situations than other e-negotiation agents in the testbed and 2) higher success rates in acquiring Grid resources under high Grid loadings.