# A remark on a helicopter and submarine game

A remark on a helicopter and submarine game The article considers a two‐person zero‐sum game in which the movement of the players is constrained to integer points …, −1, 0, 1, … of a line L. Initially the searcher (hider) is at point x = 0 (x = d, d > 0). The searcher and the hider perform simple motion on L with maximum speeds w and u, respectively, where w > u > 0. Each of the players knows the other's initial position but not the other's subsequent positions. The searcher has a bomb which he can drop at any time during his search. Between the dropping of the bomb and the bomb exploding there is a T time lag. If the bomb explodes at point i and the hider is at point i − 1, or i, or i + 1, then the destruction probability is equal to P, or 1, or P, respectively, where 0 < P < 1. d, w, u, and T are integer constants. The searcher can drop the bomb at integer moments of time t = 0, 1, … . The aim of the searcher is to maximize the probability of the destruction of the hider. © 1993 John Wiley & Sons, Inc. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Naval Research Logistics: An International Journal Wiley

# A remark on a helicopter and submarine game

9 pages

/lp/wiley/a-remark-on-a-helicopter-and-submarine-game-o36CiEdiCG
Publisher
Wiley
ISSN
0894-069X
eISSN
1520-6750
DOI
10.1002/1520-6750(199308)40:5<745::AID-NAV3220400514>3.0.CO;2-1
Publisher site
See Article on Publisher Site

### Abstract

The article considers a two‐person zero‐sum game in which the movement of the players is constrained to integer points …, −1, 0, 1, … of a line L. Initially the searcher (hider) is at point x = 0 (x = d, d > 0). The searcher and the hider perform simple motion on L with maximum speeds w and u, respectively, where w > u > 0. Each of the players knows the other's initial position but not the other's subsequent positions. The searcher has a bomb which he can drop at any time during his search. Between the dropping of the bomb and the bomb exploding there is a T time lag. If the bomb explodes at point i and the hider is at point i − 1, or i, or i + 1, then the destruction probability is equal to P, or 1, or P, respectively, where 0 < P < 1. d, w, u, and T are integer constants. The searcher can drop the bomb at integer moments of time t = 0, 1, … . The aim of the searcher is to maximize the probability of the destruction of the hider. © 1993 John Wiley & Sons, Inc.

### Journal

Naval Research Logistics: An International JournalWiley

Published: Aug 1, 1993

### References

• A One‐Dimensional Helicopter‐Submarine Game
Baston, V. J.; Bostock, F. A.

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