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Providing efficient mechanism for allocation and management of resources is essential for realizing a computational grid. Since resource providers and consumers may be independent bodies in a computing grid platform, negotiation among these participants is necessary. This position paper discusses (i) the design considerations of e-negotiation agents for grid commerce, and (ii) the possible application of Market-driven agents (MDAs) as negotiation mechanisms for managing resources in a computational grid. MDAs are negotiation agents designed with the flexibility of (i) making adjustable amounts of concession taking into account factors such as market rivalry, time preferences, and outside options, and (ii) relaxing trade expectation in the face of intense pressure. In addition to having stable strategies, making prudent compromises and optimizing utility, additional desirable properties of MDAs that are suitable for a computational grid include: adaptivity to changes in market conditions, and flexibility of reaching faster consensus.