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]**R. J. Aumann & M. Maschler, "The bargaining set for cooperative games,"*Advance in Game Theory*, M. Dresher, L. S. Shapley and A. W. Tucker, (Eds.), Annals of Mathematic Studies, No. 52, Princeton Univ. Press, Princeton, N. J., 1964, pp. 443-476. MR**0176842 (31:1114)****[2]**M. I. Balinski, "An algorithm for finding all vertices of convex polyhedral sets,"*J. Soc. Indust. Appl. Math.*, v. 9, 1961, pp. 72-88. MR**25**#5451. MR**0142057 (25:5451)****[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]**M. Davis & M. Maschler, "Existence of stable payoff configurations for cooperative games,"*Bull. Amer. Math. Soc.*, v. 69, 1963, pp. 106-108. MR**0144791 (26:2332)****[5]**J. H. Griesmer, "Extreme games with three values,"*Contributions to the Theory of Games, Vol. IV*, A. W. Tucker and R. D. Luce, (Eds.), Annals of Mathematics Studies, No. 40, Princeton Univ. Press, Princeton, N. J., 1959, pp. 189-212. MR**21**#2539. MR**0103775 (21:2539)****[6]**H. M. Gurk, "Five-person constant-sum extreme games,"*Contributions to the Theory of Games, Vol. IV*, A. W. Tucker and R. D. Luce, (Eds.), Annals of Mathematics Studies, No. 40, Princeton University Press, Princeton, N. J., 1959, pp. 179-189. MR**21**#1909. MR**0103126 (21:1909)****[7]**J. R. Isbell, "On the enumeration of majority games,"*MTAC*, v. 13, 1959, pp. 21-28. MR**21**#1912. MR**0103129 (21:1912)****[8]**R. D. Luce & H. Raiffa,*Games and Decisions*;*Introduction and Critical Survey*, Wiley, New York, 1957. MR**19**, 373. MR**0087572 (19:373e)****[9]**M. Maschler & B. Peleg, "A characterization, existence proof, and dimension bounds for the kernel of a game,"*Pacific J. Math.*(To appear.) MR**0205699 (34:5525)****[10]**J. von Neumann & O. Morgenstern,*Theory of Games and Economic Behavior*, Princeton Univ. Press, Princeton, N. J., 1944; 3rd ed., 1953. MR,**6**235; MR**9**, 50. MR**0011937 (6:235k)****[11]**B. Peleg, "Existence theorem for the bargaining set ,"*Bull. Amer. Math. Soc.*, v. 69, 1963, pp. 109-110. MR**26**#2333. MR**0144792 (26:2333)****[12]**B. Peleg, "On the kernel of constant-sum games with homogeneous weights,"*Illinois J. Math.*(To appear.) MR**0218123 (36:1212)****[13]**B. Peleg, "The kernel of -quota games,"*Canad. J. Math.*Vol. 17, 1965, pp. 239-244. MR**0178977 (31:3231)****[14]**L. S. Shapley, "Simple games: an outline of the descriptive theory,"*Behavioral Sci.*, v. 7, 1962, pp. 59-66. MR**24**#B2490. MR**0136457 (24:B2490)**

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

Article copyright:
© Copyright 1965
American Mathematical Society