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A one‐dimensional helicopter‐submarine game

Author

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  • V. J. Baston
  • F. A. Bostock

Abstract

The article considers a two‐person zero‐sum game in which a searcher with b bombs wishes to destroy a mobile hider. The players are restricted to move on a straight line with maximum speeds v and u satisfying v > u > 0; neither player can see the other but each knows the other's initial position. The bombs all have destructive radius R and there is a time lag T between the release of a bomb and the bomb exploding. The searcher gets 1 unit if the hider is destroyed and 0 if he survives. A solution is given for b = 1, and extended to b > 1 when the time lag is small. Various applications of the game are discussed.

Suggested Citation

  • V. J. Baston & F. A. Bostock, 1989. "A one‐dimensional helicopter‐submarine game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 479-490, August.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:4:p:479-490
    DOI: 10.1002/1520-6750(198908)36:43.0.CO;2-7
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    References listed on IDEAS

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    1. William H. Ruckle & John R. Reay, 1981. "Ambushing Random Walks III: More Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 121-129, February.
    2. William H. Ruckle, 1981. "Ambushing Random Walks II: Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 108-120, February.
    3. 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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