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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 College Cambridge
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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.

Information

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
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(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
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(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