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A High–Low search game on the unit interval

Published online by Cambridge University Press:  24 October 2008

V. J. Baston  and
F. A. Bostock
V. J. Baston
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO9 5NH
F. A. Bostock
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO9 5NH
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Extract

We consider the following two-person zero-sum game on the closed interval [0,1]. The hider chooses any real number h in [0,1]. The searcher successively chooses real numbers ξ1ξ2… in [0,1], where at each choice ξi he is told whether h = ξih < ξ1 or h > ξi and he may choose ξi+1 in the light of this information. The payoff (to the hider) is the sum of the distances of the searcher from the hider at each of the moves, that is .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 2 , March 1985 , pp. 345 - 348
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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