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A remark on a helicopter and submarine game

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  • Andrej Y U. Garnaev

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

Suggested Citation

  • Andrej Y U. Garnaev, 1993. "A remark on a helicopter and submarine game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(5), pages 745-753, August.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:5:p:745-753
    DOI: 10.1002/1520-6750(199308)40:53.0.CO;2-1
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    References listed on IDEAS

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    1. James N. Eagle, 1984. "The Optimal Search for a Moving Target When the Search Path Is Constrained," Operations Research, INFORMS, vol. 32(5), pages 1107-1115, October.
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