Annals of Operations Research

, Volume 215, Issue 1, pp 49–61 | Cite as

The bargaining set for sharing the power

  • Michela Chessa
  • Vito FragnelliEmail author


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 in Advances in game theory. Princeton University Press, Princeton, 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.


Power indices Bargaining set Simple games Blackmailing behavior 



The authors gratefully acknowledge some useful discussions with Guido Ortona on blackmailing issues, with Hannu Nurmi on Bargaining Set and two anonymous reviewers for their remarks and suggestions that allowed to improve the paper.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.University of MilanMilanoItaly
  2. 2.University of Eastern PiedmontAlessandriaItaly

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