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The Kernel of the General-Sum Four-Person Game

Published online by Cambridge University Press:  20 November 2018

B. Peleg
B. Peleg*
Affiliation:
The Hebrew University, Jerusalem, Israel
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In this paper we apply various results and methods of previous papers on the kernel to four-person games.

Section 2 contains the basic definitions needed. In §3 we prove that the kernel of the general-sum four-person game consists of a line segment (which may shrink to a point). A method for classifying games according to their kernels is suggested in §4 and is used there to characterize all four-person games whose kernel consists of a non-degenerate interval. In the last section, §5, we offer a bargaining procedure, based on principles established in (1), which leads to the kernel in the case of a non-degenerate interval.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 673 - 677
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Davis, M. and Maschler, M., The kernel of a cooperative game, Econometric Research Program, R-M 58, Princeton University, Princeton, N.J. (June 1963).Google Scholar
2. Hodes, L., Dense linear order and linear inequalities, Research Paper, IBM Corporation, Thomas J. Watson Research Center, Yorktown Heights, N.Y. (March 1963).Google Scholar
3. Maschler, M. and Peleg, B., A characterization, existence proof and dimension bounds for the kernel of a game; applications to the study of simple games, Research Program in Game Theory and Mathematical Economics, R-M 9, Department of Mathematics, The Hebrew University of Jerusalem, Israel (July 1964).Google Scholar
4. Shalhevet, J., On the minimal basis of a completely separating matrix, Research Program in Game Theory and Mathematical Economics, R-M 12, Department of Mathematics, The Hebrew University of Jerusalem, Israel (September 1964).Google Scholar