Abstract
A player, in a proper and monotonic simple game, is dominant if he holds a “strict majority” within a winning coalition. A (non-dictatorial) simple game is dominated if it contains exactly one dominant player. We investigate several possibilities of coalition formation in dominated simple games, under the assumption that the dominant player is given a mandate to form a coalition. The relationship between the various hypotheses on coalition formation in dominated games is investigated in the first seven sections. In the last section we classify real-life data on European parliaments and town councils in Israel.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aumann, R.J., andJ.H. Drèze: Cooperative Games with Coalition Structures. International Journal of Game Theory3, 1974, 217–237.
Aumann, R.J., B. Peleg andP. Rabinowitz: A Method for Computing the Kernel ofn-Person Games. Mathematics of Computation19, 1965, 531–551.
Axelrod, R.: Conflict of Interest. Chicago 1970.
De Swaan, A.: Coalition Theories and Cabinet Formations. Amsterdam 1973.
Isbell, J.R.: On the Enumeration of Majority Games. Mathematical Tables and Other Aids to Computation13, 1959, 21–28.
Kopelowitz, A.: Computation of the Kernels of Simple Games and the Nucleolus ofN-Person Games, RM No. 31, Research Program in Game Theory and Mathematical Economics, Department of Mathematics, The Hebrew University, Jerusalem, Israel, 1967.
Maschler, M., andB. Peleg: The Structure of the Kernel of a Cooperative Game. SIAM Journal of Applied Mathematics15, 1967, 569–604.
Maschler, M., B. Peleg andL.S. Shapley: The Kernel and Bargaining Set for Convex Games. International Journal of Game Theory1, 1972, 73–93.
Peleg, B.: A Theory of Coalition Formation in Committees. Journal of Mathematical Economics7, 1980, 115–134.
Schmeidler, D.: The Nucleolus of a Characteristic Function Game. SIAM Journal of Applied Mathematics17, 1969, 1163–1170.
Shapley, L.S.: Simple Games: An Outline of the Descriptive Theory. Behavioral Science7, 1962, 59–66.
—: A Comparison of Power Indices and a Nonsymmetric Generalization. The Rand Corporation, Santa Monica, (forthcoming), 1977.
Author information
Authors and Affiliations
Additional information
The research described in this paper was completed while the author was visiting the Department of Mathematics of the University of Hagen, D-5800 Hagen, FRG. The author is indebted to Professor O. Moeschlin for his encouragement and support.
Rights and permissions
About this article
Cite this article
Peleg, B. Coalition formation in simple games with dominant players. Int J Game Theory 10, 11–33 (1981). https://doi.org/10.1007/BF01770068
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01770068