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Technical Note—An Ambush Game with a Fat Infiltrator

School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom
School of Business Administration, University of Hyogo, Kobe 651-2197, Japan
v.j.d.baston{at}maths.soton.ac.uk
kikuta{at}biz.u-hyogo.ac.jp

This paper concerns a two-person zero-sum game between an infiltrator and a defender. The infiltrator wants to pass through a channel, while the defender wants to detect the infiltrator by laying static underwater devices across the channel. Previous work assumed the infiltrator has zero width. We consider an extension when the infiltrator has a positive width, and a proportion of its width needs to be detected by the underwater devices for a positive identification. We show that the positive-width problem reduces to the zero-width problem by an appropriate transformation.

Subject classifications: games/group decisions; noncooperative; ambush game; military; search/surveillance.
History: Received September 2006; revision received November 2007; accepted December 2007.