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 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.

[1]  Francesc Carreras,et al.  The proportional coalitional Shapley value , 2011, Expert Syst. Appl..

[2]  Forming Coalitions and Measuring Voting Power , 1982 .

[3]  A. Mas-Colell.  An equivalence theorem for a bargaining set , 1989 .

[4]  S. Hart,et al.  HANDBOOK OF GAME THEORY , 2011 .

[5]  Philip Wolfe,et al.  Contributions to the theory of games , 1953 .

[6]  A. W. Tucker,et al.  Advances in game theory , 1964 .

[7]  Martin Shubik,et al.  A Method for Evaluating the Distribution of Power in a Committee System , 1954, American Political Science Review.

[8]  David Wettstein,et al.  Equivalence between bargaining sets and the core in simple games , 1996 .

[9]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[10]  Louis J. Billera,et al.  On games without side payments arising from a general class of markets , 1974 .

[11]  Vito Fragnelli,et al.  Open Problems in veto Theory , 2013, IGTR.

[12]  Lloyd S. Shapley,et al.  On balanced sets and cores , 1967 .

[13]  M. Montero.  On the Nucleolus as a Power Index , 2013 .

[14]  Michael Maschler,et al.  The inequalities that determine the bargaining setM1(i) , 1966 .

[15]  Lin Zhou,et al.  A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation , 1994 .

[16]  L. Shapley.  A Value for n-person Games , 1988 .

[17]  M. Maschler.  The bargaining set, kernel, and nucleolus , 1992 .

[18]  Ron Johnston,et al.  On the Measurement of Power: Some Reactions to Laver , 1978 .

[19]  J. Deegan,et al.  A new index of power for simplen-person games , 1978 .

[20]  R. Aumann,et al.  THE BARGAINING SET FOR COOPERATIVE GAMES , 1961 .