Affiliations: [a] Department of Mathematics and Computer Science, University of Calabria, Italy. E-mails: alviano@mat.unical.it, ggreco@mat.unical.it | [b] Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, University of Calabria, Italy. E-mail: guzzo@dimes.unical.it
Note: [1] A preliminary version of parts of this paper was presented at the AT 2016 Conference.
Abstract: Coalition formation is studied in a setting where agents take part to a group decision-making scenario and where their preferences are expressed via weighted propositional logic, in particular by considering formulas consisting of conjunctions of literals only. Interactions among agents are constrained by an underlying social environment and each agent is associated with a specific social factor determining to which extent she prefers staying in a coalition with other agents. In particular, the utilities of the agents depend not only on their absolute preferences but also on the number of “neighbors” occurring with them in the coalition that emerged. Within this setting, the computational complexity of a number of relevant reasoning tasks is studied, by charting a clear picture of the intrinsic difficulty of finding “agreements” among the agents. Specific algorithmic approaches to reason about such social environments are proposed under the utilitarian perspective, where the collective utility of a coalition is the sum of the utilities of the individuals, as well as under the egalitarian perspective, with the goal being to maximize the utility of the least satisfied agent. These algorithms have been implemented and results of experimental activity are discussed, too.
