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On games with almost complete information

Published online by Cambridge University Press:  24 October 2008

B. J. Birch
B. J. Birch
Affiliation:
Trinity CollegeCambridge
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Extract

1. It is well known that a game with perfect information has an equilibrium-point of pure strategies; this was first proved for two-person games by Zermelo (9), and later extended to n-person games by Kuhn(3). More recently, Dalkey(1) and Otter and Dunne (8) have published the stronger result (Theorem 6 below): If in the complete inflation of a game Γ every player has complete information about every other player, then Γ has an equilibrium-point of pure strategies.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 2 , April 1955 , pp. 275 - 287
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

(1)Dalkey, N. Equivalence of information patterns, and essentially determinate games. Contributions to the theory of games, vol. 2 (Ann. Math. Stud, no 28, Princeton, 1953), pp. 217–45.Google Scholar
(2)Gale, D.A theory of n–person games with perfect information. Proc. nat. Acad. Sci., Wash., 39 (1953), 496–501.Google Scholar
(3)Kuhn, H. W.Extensive Games. Proc. nat. Acad. Sci., Wash., 36 (1950), 570–6.Google Scholar
(4)Kuhn, H. W. Extensive Games and the problem of information. Contributions to the theory of games, vol. 2 (Ann. Math. Stud. no. 28, Princeton, 1953), pp. 193–216Google Scholar
(5)Nash, J. F.Equilibrium points in n-person games. Proc. nat. Acad. Sci., Wash., 36 (1950), 48–9.CrossRefGoogle ScholarPubMed
(6)Nash, J. F.Non-cooperative games. Ann. Math., Princeton, 54 (1951), 286–95.Google Scholar
(7)Von Neumann, J. and Morgenstern, O.Theory of games and economic behaviour (Princeton, 1947).Google Scholar
(8)Otter, R. and Dunne, J.Games with Equilibrium-points. Proc. nat. Acad. Sci., Wash., 39 (1953), 310–14.Google Scholar
(9)Zermelo, E. Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. Proc. Fifth int. Congr. Math. Cambridge 1912, vol. 2, p. 501.Google Scholar