Abstract. The Agent in Grid (AiG) project attempts to integrate the concept of the Grid and an agent-based system to facilitate efficient resource management in the Grid. In this paper, we present preliminary considerations concerning multiple equivalent simultaneous offers strategy that can be used in the Service Level Agreement (SLA) negotiations. These negotiations are the key part of the main use case scenarios within the AiG project. In this context, first, we describe the AiG system. Second, we introduce the simultaneous offer strategy, as a mechanism known from economy, and suggest an approach for using it in the AiG negotiations.Key words: Grid computing, multiple equivalent simultaneous offers, AiG, agent-based negotiations, SLA, multi-attribute negotiations 1. Introduction. The context for the presented work is provided by the Agents in Grid project (AiG; [16,17,23]) that aims at creating a management system for the Grid computing resources. The system utilizes the concept of software agents that can act flexibly in a dynamic and uncertain environment, where resources can appear and disappear at any time. Furthermore, the AiG project integrates business principles, by allowing users to earn money by offering resources, or to pay for the use of available resources. The key part of the realization of this economic model is the negotiation process that should lead to contracts beneficial to the engaged parties. In the AiG project, negotiations materialize in the two main scenarios: (i) when the user would like to execute her job and is searching for resources that satisfy her needs, (ii) when a resource owner is seeking a team to join, to earn money. Here, we are confronted with one of the key assumptions behind the AiG project. Based on the analysis of working conditions of volunteer systems (e.g. seti@home; [32]), and taking into account progress in the development of agent systems (their capability for autonomously reaching an agreement [33]) it was stipulated that agents that offer their resources to earn money should work in teams. In this way, teams should be able to deliver results even if some members disappear without warning (for more details, see [16]).Observe that negotiations taking place in the AiG project have to take into account multiple attributes. In an example given in [23] simple job execution negotiations involved simultaneous evaluation of price, job start time and job end time. Currently, after the AiG ontology was fully developed (see, [22] for more details), truly multi-criterial negotiations can be used. Note that in both negotiation scenarios introduced above, the negotiation strategy is constrained by the following conditions: (1) no information about the preferences of the other participant(s) in the negotiation, and (2) the agreement reached should be optimal to both negotiating parties.Let us observe that recent studies in social psychology and economics [1,2] have shown that using a strategy based on multiple offers is more profitable than a strategy based on a single offe...