Axiomatizations of the normalized Banzhaf value and the Shapley value

被引:54
作者
van den Brink, R
van der Laan, G
机构
[1] Tilburg Univ, Dept Econometr, NL-5000 LE Tilburg, Netherlands
[2] Free Univ Amsterdam, Dept Econometr, NL-1081 HV Amsterdam, Netherlands
[3] Free Univ Amsterdam, Tinbergen Inst, NL-1081 HV Amsterdam, Netherlands
关键词
Cooperative Game; Solution Concept; Grand Coalition; Transferable Utility; Similar Axiom;
D O I
10.1007/s003550050125
中图分类号
F [经济];
学科分类号
02 ;
摘要
A cooperative game with transferable utilities - or simply a TU-game - describes a situation in which players can obtain certain payoffs by cooperation. A solution concept for these games is a function which assigns to every such a game a distribution of payoffs over the players in the game. Famous solution concepts for TU-games are the Shapley value and the Banzhaf value. Both solution concepts have been axiomatized in various ways. An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the 'grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient. In this pager we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the 'grand coalition' proportional to the Banzhaf values of the players. This value does not satisfy certain axioms underlying the Banzhaf value. In this paper we introduce some new axioms that characterize the normalized Banzhaf value. We also provide an axiomatization of the Shapley value using similar axioms.
引用
收藏
页码:567 / 582
页数:16
相关论文
共 10 条
[1]  
Banzhaf JF, 1965, Rutgers Law Review, V19, P317
[2]  
DERKS J, 1994, NULL PLAYERS OUT
[3]  
Dubey P., 1979, Mathematics of Operations Research, V4, P99, DOI 10.1287/moor.4.2.99
[4]   COLLUSION PROPERTIES OF VALUES [J].
HALLER, H .
INTERNATIONAL JOURNAL OF GAME THEORY, 1994, 23 (03) :261-281
[5]  
Harsanyi J. C., 1959, Contribution to the Theory of Games IV, V2, P325
[6]   AN AXIOMATIZATION OF THE BANZHAF VALUE [J].
LEHRER, E .
INTERNATIONAL JOURNAL OF GAME THEORY, 1988, 17 (02) :89-99
[7]  
Shapley L S, 1953, VALUE N PERSON GAMES, V28, P307, DOI DOI 10.7249/P0295
[8]  
VANDENBRINK R, 1995, 895249 TI FREE U
[9]  
VANDERLAAN G, IN PRESS THEORY DECI
[10]  
Young H. P., 1985, International Journal of Game Theory, V14, P65, DOI 10.1007/BF01769885