On the Coalitional Rationality of the Banzhaf Value and Other Non-Efficient Semivalues

DOI: 10.4236/am.2015.612182   PDF   HTML   XML   1,831 Downloads   2,103 Views   Citations


In the Inverse Set relative to a Semivalue, we are looking for a new game for which the Semivalue of the original game is coalitional rational. The problem is solved by means of the Power Game of the given game. The procedures of building the new game, as well as the case of the Banzhaf Value are illustrated by means of some examples.

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Dragan, I. (2015) On the Coalitional Rationality of the Banzhaf Value and Other Non-Efficient Semivalues. Applied Mathematics, 6, 2069-2076. doi: 10.4236/am.2015.612182.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Dragan, I. (1991) The Potential Basis and the Weighted Shapley Value. Libertas Mathematica, 11, 139-146.
[2] Dragan, I. (2005) On the Inverse Problem for Semivalues of Cooperative TU Games. IJPAM, 4, 545-561.
[3] Dragan, I. (2014) On the Coalitional Rationality of the Shapley Value and Other Efficient Values. AJOR, 4, 228-234.
[4] Banzhaf, J.F. (1965) Weighted Voting Doesn’t Work: A Mathematical Analysis. Rutgers Law Review, 19, 317-343.
[5] Dubey, P., Neyman, A. and Weber, R.J. (1981) Value Theory without Efficiency. Mathematics of Operations Research, 6, 122-128.
[6] Dragan, I. and Martinez-Legaz, J.E. (2001) On the Semivalues and the Power Core of Cooperative TU Games. IGTR, 3, 127-139.
[7] Dragan, I. (1996) On Some Relationships between the Shapley Value and the Banzhaf Value. Libertas Mathematica, 16, 31-42.
[8] Puente, M.A. (2000) Contributions to the Representability of Simple Games and to the Calculus of Solutions for This Class of Games. Ph.D. Thesis, Technical University of Catalonia.
[9] Dragan, I. (2014) Coalitional Rationality and the Inverse Problem for Binomial Semivalues, In: Petrosjan, L. and Zenkevich, N., Eds., Contributions to Game Theory and Management, Vol. 7, 24-33.

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