A value for games with a coalition structure is introduced, where the rules guiding cooperation among the members of the same coalition are different from the interaction rules among coalitions. In particular, players inside a coalition exhibit a greater degree of solidarity than they are willing to use with players outside their coalition. The Shapley value is therefore used to compute the aggregate payoffs for the coalitions, and the solidarity value to obtain the payoffs for the players inside each coalition.

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Network expansion planning is a complex, nonconvex, combinatorial problem. Different techniques, such as mathematical optimization, heuristics, and metaheuristics, have been traditionally used to solve this problem. This paper presents a new model, ANDREA, which is intended to obtain near optimal networks for both the static and dynamic planning. This tool has been developed to determine when and where new lines and transformers have to be installed in subtransmission real size networks to supply the estimated future demand considering security of supply criteria, with a low computational effort. A fast guided tree search algorithm (GTSA) using smart selection criteria has been designed to solve this problem. Comparison of the obtained results has been made with those provided by a slower genetic algorithm (GA). Both algorithms were tested in a real subtransmission network.