VALUES FOR 2-STAGE GAMES - ANOTHER VIEW OF THE SHAPLEY AXIOMS

被引:4
作者
BEJA, A
GILBOA, I
机构
[1] MIT,CAMBRIDGE,MA 02139
[2] NORTHWESTERN UNIV,JL KELLOGG GRAD SCH MANAGEMENT,DEPT MANAGERIAL ECON & DECIS SCI,EVANSTON,IL 60201
关键词
Majority Games; Shapley Axioms; Shapley Values; Two-Stage Games;
D O I
10.1007/BF01753705
中图分类号
F [经济];
学科分类号
02 ;
摘要
This short study reports an application of the Shapley value axioms to a new concept of "two-stage games." In these games, the formation of a coalition in the first stage entitles its members to play a prespecified cooperative game at the second stage. The original Shapley axioms have natural equivalents in the new framework, and we show the existence of (non-unique) values and semivalues for two stage games, analogous to those defined by the corresponding axioms for the conventional (one-stage) games. However, we also prove that all semivalues (hence, perforce, all values) must give patently unacceptable solutions for some "two-stage majority games" (where the members of a majority coalition play a conventional majority game). Our reservations about these prescribed values are related to Roth's (1980) criticism of Shapley's "λ-transfer value" for non-transferable utility (NTU) games. But our analysis has wider scope than Roth's example, and the argument that it offers appears to be more conclusive. The study also indicates how the values and semivalues for two-stage games can be naturally generalized to apply for "multi-stage games." © 1990 Physica-Verlag.
引用
收藏
页码:17 / 31
页数:15
相关论文
共 14 条
[1]   ON THE NONTRANSFERABLE UTILITY VALUE - REJOINDER [J].
AUMANN, RJ .
ECONOMETRICA, 1986, 54 (04) :985-989
[2]   ON THE NON-TRANSFERABLE UTILITY VALUE - A COMMENT ON THE ROTH-SHAFER EXAMPLES [J].
AUMANN, RJ .
ECONOMETRICA, 1985, 53 (03) :667-677
[3]   AN AXIOMATIZATION OF THE NON-TRANSFERABLE UTILITY VALUE [J].
AUMANN, RJ .
ECONOMETRICA, 1985, 53 (03) :599-612
[4]   VALUES OF MARKETS WITH A CONTINUUM OF TRADERS [J].
AUMANN, RJ .
ECONOMETRICA, 1975, 43 (04) :611-646
[5]   VALUE THEORY WITHOUT EFFICIENCY [J].
DUBEY, P ;
NEYMAN, A ;
WEBER, RJ .
MATHEMATICS OF OPERATIONS RESEARCH, 1981, 6 (01) :122-128
[6]  
Ford L., 1962, FLOWS NETWORKS
[7]   VALUES FOR GAMES WITHOUT SIDE PAYMENTS - COMMENT [J].
HARSANYI, JC .
ECONOMETRICA, 1980, 48 (02) :477-477
[8]   NON-TRANSFERABLE UTILITY GAMES AND MARKETS - SOME EXAMPLES AND THE HARSANYI SOLUTION [J].
HART, S .
ECONOMETRICA, 1985, 53 (06) :1445-1450
[9]   AN AXIOMATIZATION OF HARSANYIS NON-TRANSFERABLE UTILITY SOLUTION [J].
HART, S .
ECONOMETRICA, 1985, 53 (06) :1295-1313
[10]   VALUES FOR GAMES WITHOUT SIDEPAYMENTS - SOME DIFFICULTIES WITH CURRENT CONCEPTS [J].
ROTH, AE .
ECONOMETRICA, 1980, 48 (02) :457-465