Abstract
In this paper, we considern-person weighted majority games with major and minor players. We prove under certain conditions that if the minor players split into equal “mini-minor” players the nucleolus' components which correspond to the major players do not change.
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Davis, M., andM. Maschler: The kernel of a cooperative game. Naval Res. Logistics Quar.12, 223–259, 1965.
Maschler, M., andB. Peleg: A characterization, existence proof and dimensions bounds for the kernel of a game. Pacific J. Math.18, 289–328, 1966.
Peleg, B.: On weights of constant-sum majority games. SIAM J. Appl. Math.16, 527–532, 1968.
Schmeidler, D.: The nucleolus of a characteristic function game. SIAM J. Appl. Math.17, 1163–1170, 1969.
Shapley, L. S.: Simple games; an outline of the descriptive theory. Behavioral Science7, 59–66, 1962.
Shapley, L. S., and J. W.Milnor: Values of large games, II: Oceanic games. The Rand Corporation, RM 2649, February 1961.
— —: The structure of the kernel of a cooperative game. SIAM J. Appl. Math.15, 569–604, 1967.
Shapley, L. S., and N. Z.Shapiro: Values of large games, I: A limit theorem. The Rand Corporation, RM 2648, November 1960.
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This paper is a part of the author's M. Sc. thesis prepared at Tel-Aviv University under the direction of Professor R. J.Aumann.
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Galil, Z. The nucleolus in games with major and minor players. Int J Game Theory 3, 129–140 (1974). https://doi.org/10.1007/BF01763253
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DOI: https://doi.org/10.1007/BF01763253