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Recursive matrix games

Published online by Cambridge University Press:  14 July 2016

Michael Orkin
Michael Orkin*
Affiliation:
Case Western Reserve University, Cleveland, Ohio
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Abstract

“Recursive” games were first defined and studied by Everett. Related results can be found in Gillette, Milnor and Shapley, and Blackwell and Ferguson. In this paper we introduce the notion of a recursive matrix game, which we believe eliminates the vagueness but none of the useful generality of the earlier definition. We then give an inductive proof (different from the proof in [3]) that these games have a value, with ∊-optimal stationary strategies available to each player. We also apply the result and show how a class of games studied in a different framework are games of this type and thus have a value.

Keywords

STOCHASTIC GAMESMATRIX GAMEZERO SUMINFINITE GAMERANDOM STRATEGYTWO PERSON GAMECOL. BLOTTO GAMEGAMES WITH IMPEREFCT INFORMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 813 - 820
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Blackwell, D. (1969) Infinite Gd games with imperfect information. Zastos. Mat. Applicationes Mathematicae, Hugo Steinhaus Jubilee Volume.Google Scholar
[2] Blackwell, D. and Ferguson, T. S. (1968) The big match. Ann. Math. Statist. 39, 159–163.Google Scholar
[3] Everett, H. (1957) Recursive games. Contributions to the Theory of Games, 3, 47–78.Google Scholar
[4] Gillette, D. (1957) Stochastic games with zero stop probabilities. Contributions to the Theory of Games, 3, 179–187.Google Scholar
[5] Milnor, J. and Shapley, L. S. (1957) On games of survival. Contributions to the Theory of Games, 3, 15–45.Google Scholar