A banzhaf share function for cooperative games in coalition structure

Theory and Decision

Volumn 53, Issue 1, 2002, Pages 61-86

  Van Der Laan, Gerard ^a   Van Den Brink, René ^a  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Banzhaf share function; Coalition structure; Consistency; Multiplication property; TU game

Indexed keywords

DECISION THEORY; NUMERICAL METHODS; OPTIMIZATION; SET THEORY; THEOREM PROVING;

BANZHAF SHARE FUNCTION; COALITION STRUCTURE; CONSISTENCY; COOPERATIVE GAMES; MULTIPLICATION PROPERTY; TRANSFERABLE UTILITY GAME;

GAME THEORY;

EID: 0036704119     PISSN: 00405833     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020805106965     Document Type: Article

References (23)

1. Aumann, R.J. and Drèze, J.H. (1974), Cooperative games with coalition structure, International Journal of Game Theory, 3: 217-237.
2. Banzhaf, J.F. (1965), Weighted voting doesn't work: A mathematical analysis, Rutgers Law Review, 19: 317-343.
3. Brink, R. van den and Laan, G. van der (1998a), Axiomatizations of the normalized Banzhaf value and the Shapley value, Social Choice and Welfare, 15: 567-582.
4. Brink, R. van den and Laan, G. van der (1998b), The normalized Banzhaf value and the Banzhaf share function, in: L.A. Petrosjan and V.V. Mazalov (eds.), Game Theory and Applications IV, pp. 11-31, Nova Science Publishers, New York.
5. Brink, R. van den and Laan, G. van der (2001), A class of consistent share functions for cooperative games in coalition structure, Tinbergen Institute, Discussion Paper 2001-44/1.
6. Carreras, F. and Magaña, A. (1994), The multilinear extension and the modified Banzhaf-Coleman index, Mathematical Social Sciences, 28: 215-222.
7. Davis, M., and Maschler, M. (1965), The kernel of a cooperative game, Naval Research Logistics Quarterly 12: 223-259.
8. Dubey, P. and Shapley, L.S. (1979), Mathematical properties of the Banzhaf power index, Mathematics of Operations Research 4: 99-131.
9. Grabisch, M., and Roubens, M. (1999) An axiomatic approach to the concept of interaction among players in cooperative games, International Journal of Game Theory 28: 547-565.
10. Haller, H. (1994), Collusion properties of values, International Journal of Game Theory, 23: 261-281.
11. Hammer, P.L. and Holzman, R. (1992) Approximations of pseudo-Boolean functions; applications to game theory, ZOR - Methods and Models of Operations Research 36: 3-21.
12. Hart, S. and Kurz, M. (1983), Endogenous formation of coalitions, Econometrica 51: 1047-1064.
13. Laan, G. van der, and Brink, R. van den (1998), Axiomatization of a class of share functions for N-person games, Theory and Decision 44: 117-148.
14. Lehrer, E. (1988), An axiomatization of the Banzhaf value, International Journal of Game Theory 17: 89-99.
15. Nowak, A.S (1997), On the axiomatization of the Banzhaf value without the additivity axiom, International Journal of Game Theory 26: 137-141.
16. Shapley, L.S. (1953), A value for n-person games, in: H.W. Kuhn and A.W. Tucker (eds.), Contributions to the Theory of Games, Vol. II, (Annals of Mathematics Studies 28), pp. 307-317, Princeton University Press, Princeton.
17. Owen, G. (1972), Multilinear extensions of games, Management Sciences 18: 64-79.
18. Owen, G. (1975), Multilinear extensions and the Banzhaf value, Naval Research Logistics Quart. 22: 741-750.
19. Owen, G. (1977), Values of games with a priori unions, in: R. Hein and O. Moeschlin (eds.), Essays in Mathematical Economics and Game Theory, pp. 76-78, Springer, New York.
20. Owen, G. (1981), Modification of the Banzhaf-Coleman index for games with a priori unions, in: M.J. Holler (ed.), Power, Voting, and Voting Power, pp. 232-238, Physica-Verlag, Würzburg, Germany.
21. Owen, G. and Winter, E. (1992), The multilinear extension and the coalition structure value, Games and Economic Behavior, 4: 582-587.
22. Winter, E. (1989), A value for cooperative games with levels structure of cooperation, International Journal of Game Theory 18: 227-240.
23. Winter, E. (1992), The consistency and potential for values of games with coalition structure, Games and Economic Behavior 4: 132-144.