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New results on a stochastic duel game with each force consisting of heterogeneous units

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  • Kyle Y. Lin

Abstract

Two forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force—knowing which units are still alive in real time—decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two‐person zero‐sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This article gives an iterative algorithm to compute the optimal strategy without having to enumerate the entire payoff matrix, and offers some insights into the special case, where one force has only one unit. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 56–65, 2014

Suggested Citation

  • Kyle Y. Lin, 2014. "New results on a stochastic duel game with each force consisting of heterogeneous units," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 56-65, February.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:1:p:56-65
    DOI: 10.1002/nav.21566
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    References listed on IDEAS

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    1. Kensaku Kikuta, 1986. "The matrix game derived from the many‐against‐many battle," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 603-612, November.
    2. Richard H. Brown, 1963. "Theory of Combat: The Probability of Winning," Operations Research, INFORMS, vol. 11(3), pages 418-425, June.
    3. M Kress & I Talmor, 1999. "A new look at the 3:1 rule of combat through Markov Stochastic Lanchester models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 733-744, July.
    4. Kensaku Kikuta, 1983. "Technical Note—A Note on the One Against Many Battle," Operations Research, INFORMS, vol. 31(5), pages 952-956, October.
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