A method for computing the kernel of -person games

Authors:
R. J. Aumann, B. Peleg and P. Rabinowitz

Journal:
Math. Comp. **19** (1965), 531-551

MSC:
Primary 90.70

DOI:
https://doi.org/10.1090/S0025-5718-1965-0198988-7

MathSciNet review:
0198988

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References | Similar Articles | Additional Information

**[1]**Robert J. Aumann and Michael Maschler,*The bargaining set for cooperative games*, Advances in Game Theory, Princeton Univ. Press, Princeton, N.J., 1964, pp. 443–476. MR**0176842****[2]**M. L. Balinski,*An algorithm for finding all vertices of convex polyhedral sets*, J. Soc. Indust. Appl. Math.**9**(1961), 72–88. MR**0142057****[3]**M. Davis & M. Maschler,*The Kernel of a Cooperative Game*, Research Memorandum No. 58, Econometric Research Program, Princeton University, Princeton, N. J., June, 1963.**[4]**Morton Davis and Michael Maschler,*Existence of stable payoff configurations for cooperative games*, Bull. Amer. Math. Soc.**69**(1963), 106–108. MR**0144791**, https://doi.org/10.1090/S0002-9904-1963-10879-4**[5]**James H. Griesmer,*Extreme games with three values*, Contributions to the theory of games, Vol. IV, Annals of Mathematics Studies, no. 40, Princeton University Press, Princeton, N.J., 1959, pp. 189–212. MR**0103775****[6]**Herbert M. Gurk,*Five-person, constant-sum, extreme games*, Contributions to the theory of games, Vol. IV, Annals of Mathematics Studies, no. 40, Princeton University Press, Princeton, N.J., 1959, pp. 179–188. MR**0103126****[7]**John R. Isbell,*On the enumeration of majority games*, Math. Tables Aids Comput.**13**(1959), 21–28. MR**0103129**, https://doi.org/10.1090/S0025-5718-1959-0103129-5**[8]**R. Duncan Luce and Howard Raiffa,*Games and decisions: introduction and critical survey*, John Wiley & Sons, Inc., New York, N. Y., 1957. A study of the Behavioral Models Project, Bureau of Applied Social Research, Columbia University;. MR**0087572****[9]**M. Maschler and B. Peleg,*A characterization, existence proof and dimension bounds for the kernel of a game*, Pacific J. Math.**18**(1966), 289–328. MR**0205699****[10]**John von Neumann and Oskar Morgenstern,*Theory of Games and Economic Behavior*, Princeton University Press, Princeton, New Jersey, 1944. MR**0011937****[11]**Bezalel Peleg,*Existence theorem for the bargaining set 𝑀₁⁽ⁱ⁾*, Bull. Amer. Math. Soc.**69**(1963), 109–110. MR**0144792**, https://doi.org/10.1090/S0002-9904-1963-10881-2**[12]**Bezalel Peleg,*On the kernel of constant-sum simple games with homogeneous weights*, Illinois J. Math.**10**(1966), 39–48. MR**0218123****[13]**Bezalel Peleg,*The kernel of 𝑚-quota games*, Canad. J. Math.**17**(1965), 239–244. MR**0178977**, https://doi.org/10.4153/CJM-1965-022-x**[14]**L. S. Shapley,*Simple games: an outline of the descriptive theory*, Behavioral Sci.**7**(1962), 59–66. MR**0136457**, https://doi.org/10.1002/bs.3830070104

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DOI:
https://doi.org/10.1090/S0025-5718-1965-0198988-7

Article copyright:
© Copyright 1965
American Mathematical Society