The Bargaining Set for Sharing the Power

The evaluation of the power of the parties of a Parliament is usually carried out following a static approach, counting their numbers of seats and possible ideological relations among them. In this paper we propose a dynamic model in which parties may blackmail each other in order to increase their power at the expense of others. This model may be solved in terms of the Bargaining Set (Aumann and Maschler, 1964), a set valued solution, in contrast to the classical power indices that are point valued; so it may be used to check the robustness of a power division taking into account possible blackmailing activities. The paper is mainly based on the idea of proposing an existing instrument, the Bargaining Set, as power index to analyze this blackmailing situation. The computational complexity limits the possibility of applying it to real-world situations, but the possibility of making the computation easier is shown using some examples.