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Combined negotiation in multi-agent systems is a hard task since it involves several levels of difficulty. In order to improve their payoff, first agents behave in a strategic manner while bargaining since they need to deal with various types of behaviors. Second agents have to react to the proposals of other agents in finding the optimal solutions for their negotiation. This paper tackles the problem of winner determination in combined multi-agent negotiations and addresses two fundamental issues. The first contribution of this work is a winner determination algorithm, which finds an optimal solution, which is a combination of several bids selected from a set of bids at one iteration of a combined negotiation. In addition, the problem of dynamically revising these optimal solutions with regards to changes on bids is considered. These changes occur in multi-agent negotiation processes having several iterations and which use multi-phased protocols. To date no work addresses this problem. The second contribution of this work is an iterative algorithm for updating the optimal solutions to avoid integral and repetitive reapplication of the winner determination algorithm. The results of the experiments carried out using our algorithms have confirmed the importance and the originality of our approach based on the use of shared and unshared item graphs.
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