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Algorithms for finding coalitions exploiting a new reciprocity condition. (English) Zbl 1186.68447
Summary: We introduce a reciprocity criterion for coalition formation among goal-directed agents, which we call the indecomposable do-ut-des property. It refines an older reciprocity property, called the do-ut-des or give-to-get property by considering the fact that agents prefer to form coalitions whose components cannot be formed independently. A formal description of this property is provided as well as an analysis of algorithms and their complexity. We provide an algorithm to decide whether a coalition has the desired property, and we show that the problem to verify whether a single coalition satisfies the property is tractable. Moreover, we provide an algorithm to search all the sub-coalitions of a given coalition satisfying the new property. Even if this problem is not computationally tractable, we show that in several cases, also the complexity of this problem may decrease considerably.
68T27 Logic in artificial intelligence
91A12 Cooperative games
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