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The bargaining set for sharing the power

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  • Michela Chessa
  • Vito Fragnelli

Abstract

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Michela Chessa & Vito Fragnelli, 2014. "The bargaining set for sharing the power," Annals of Operations Research, Springer, vol. 215(1), pages 49-61, April.
    • Handle: RePEc:spr:annopr:v:215:y:2014:i:1:p:49-61:10.1007/s10479-013-1411-7
    DOI: 10.1007/s10479-013-1411-7
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    References listed on IDEAS

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    1. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    2. Michela Chessa & Vito Fragnelli, 2013. "Open Problems In Veto Theory," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-15.
    3. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    4. R J Johnston, 1978. "On the Measurement of Power: Some Reactions to Laver," Environment and Planning A, , vol. 10(8), pages 907-914, August.
    5. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    7. Einy, Ezra & Wettstein, David, 1996. "Equivalence between Bargaining Sets and the Core in Simple Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 65-71.
    8. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
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    Cited by:

    1. Vito Fragnelli & Gianfranco Gambarelli, 2014. "Further open problems in cooperative games," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(4), pages 51-62.

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