Book Review
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MathSciNet review:
1566765
Full text of review:
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Book Information:
Authors:
R. J. Aumann and
L. S. Shapley
Title:
Values of non-atomic games
Additional book information:
Princeton University Press, Princeton, New Jersey, 1974, xi+333 pp., $14.50.
R. J. Aumann and M. Perles, A variational problem arising in economics, J. Math. Anal. Appl. 11 (1965), 488–503. MR 182447, DOI 10.1016/0022-247X(65)90100-9
R. J. Aumann and L. S. Shapley, Values of non-atomic games, Princeton University Press, Princeton, N.J., 1974. A Rand Corporation Research Study. MR 0378865
John C. Harsanyi, A bargaining model for the cooperative $n$-person game, Contributions to the theory of games, Vol. IV, Annals of Mathematics Studies, no. 40, Princeton University Press, Princeton, N.J., 1959, pp. 325–355. MR 0105320
4. J. C. Harsanyi, A simplified bargaining model for the n-person cooperative game, Internat. Economic Review 4 (1963), 194-220.
Werner Hildenbrand, Core and equilibria of a large economy, Princeton Studies in Mathematical Economics, No. 5, Princeton University Press, Princeton, N.J., 1974. With an appendix to Chapter 2 by K. Hildenbrand. MR 0389160
J. R. Isbell, Absolute games, Contributions to the theory of games, Vol. IV, Annals of Mathematics Studies, no. 40, Princeton University Press, Princeton, N.J., 1959, pp. 357–396. MR 0134359
J. R. Isbell, A modification of Harsanyi’s bargaining model, Bull. Amer. Math. Soc. 66 (1960), 70–73. MR 122591, DOI 10.1090/S0002-9904-1960-10398-9
John R. Isbell, Contract law and the value of a game, Israel J. Math. 5 (1967), 135–144. MR 246643, DOI 10.1007/BF02771099
William F. Lucas, The proof that a game may not have a solution, Trans. Amer. Math. Soc. 137 (1969), 219–229. MR 237183, DOI 10.1090/S0002-9947-1969-0237183-X
John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, N.J., 1944. MR 0011937
Reinhard Selten, Valuation of $n$-person games, Advances in Game Theory, Princeton Univ. Press, Princeton, N.J., 1964, pp. 577–626. MR 0163781
L. S. Shapley, A value for $n$-person games, Contributions to the theory of games, vol. 2, Annals of Mathematics Studies, no. 28, Princeton University Press, Princeton, N.J., 1953, pp. 307–317. MR 0053477
L. S. Shapley, A solution containing an arbitrary closed component, Contributions to the theory of games, Vol. IV, Annals of Mathematics Studies, no. 40, Princeton University Press, Princeton, N.J., 1959, pp. 87–93. MR 0109749
14. L. S. Shapley, Values of large market games: Status of the problem, RM-3957-PR, The Rand Corporation, Santa Monica, 1964.
- 1.
- R. J. Aumann and M. Perles, A variational problem arising in economics, J. Math. Anal. Appl. 11 (1965), 488-503. MR 31 #6670. MR 0182447
- 2.
- R. J. Aumann and L. S. Shapley, Values of non-atomic games. Part I: The axiomatic approach, RM-5468-PR, The Rand Corporation, Santa Monica; also RM-42, The Hebrew University of Jerusalem, 1968. MR 378865
- 3.
- J. C. Harsanyi, A bargaining model for the cooperative n-person game, Contributions to the Theory of Games, vol. 4, Princeton Univ. Press, Princeton, N.J., 1959, pp. 325-355. MR 21 #4062. MR 105320
- 4.
- J. C. Harsanyi, A simplified bargaining model for the n-person cooperative game, Internat. Economic Review 4 (1963), 194-220.
- 5.
- W. Hildenbrand, Core and equilibria of a large economy, Princeton Univ. Press, Princeton, N.J., 1974. MR 389160
- 6.
- J. R. Isbell, Absolute games, Contributions to the Theory of Games, vol. 4, Princeton Univ. Press, Princeton, N.J., 1959, pp. 357-396. MR 24 #B412. MR 134359
- 7.
- J. R. Isbell, A modification of Harsanyi's bargaining model, Bull. Amer. Math. Soc. 66 (1960), 70-73. MR 22 #13315. MR 122591
- 8.
- J. R. Isbell, Contract law and the value of a game, Israel J. Math. 5 (1967), 135-144. MR 39 #7947. MR 246643
- 9.
- W. F. Lucas, The proof that a game may not have a solution, Trans. Amer. Math Soc. 137 (1969), 219-229. MR 38 #5474. MR 237183
- 10.
- J. von Neumann and O. Morgenstern, Theory of games and economic behavior, Princeton Univ. Press, Princeton, N.J., 1944. MR 6, 235. MR 11937
- 11.
- R. Selten, Valuation of n-person games, Advances in Game Theory, Princeton, N.J., 1964, pp. 577-626. MR 29 #1081. MR 163781
- 12.
- L. S. Shapley, A value for n-person games, Contributions to the Theory of Games, vol. 2, Princeton Univ. Press, Princeton, N.J., 1953, pp. 307-317. MR 14, 779. MR 53477
- 13.
- L. S. Shapley, A solution containing an arbitrary closed component, Contributions to the Theory of Games, vol. 4, Princeton Univ. Press, Princeton, N.J., 1959, pp. 87-94. MR 22 #635. MR 109749
- 14.
- L. S. Shapley, Values of large market games: Status of the problem, RM-3957-PR, The Rand Corporation, Santa Monica, 1964.
Review Information:
Reviewer:
J. R. Isbell
Journal:
Bull. Amer. Math. Soc.
81 (1975), 539-546
DOI:
https://doi.org/10.1090/S0002-9904-1975-13732-3