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Discretization of the continuous ambush game

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  • I.D. Woodward

Abstract

This article further considers the two‐person continuous ambush game introduced by Ruckle. This article extends the work of Ruckle, Baston and Bostock, and Lee by considering the game for a general number of barriers. By supplanting optimal strategies from a discretized version of the game, we show that there always exists a value for the game, which, furthermore, can be found using linear programming techniques. Further to this, we show that the discrete ambush game considered by Garnaev has the same value as a continuous game, allowing many new results to be obtained in both games. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 515–529, 2003

Suggested Citation

  • I.D. Woodward, 2003. "Discretization of the continuous ambush game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 515-529, August.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:5:p:515-529
    DOI: 10.1002/nav.10066
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    References listed on IDEAS

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    1. V. J. Baston & F. A. Bostock, 1987. "A continuous game of ambush," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 645-654, October.
    2. Zoroa, Noemi & Zoroa, Procopio & Jose Fernandez-Saez, M., 1999. "A generalization of Ruckle's results for an ambush game," European Journal of Operational Research, Elsevier, vol. 119(2), pages 353-364, December.
    3. William H. Ruckle & John R. Reay, 1981. "Ambushing Random Walks III: More Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 121-129, February.
    4. K. T. Lee, 1990. "On ruckle's game of ambush," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 355-363, June.
    5. William Ruckle & Robert Fennell & Paul T. Holmes & Charles Fennemore, 1976. "Ambushing Random Walks I: Finite Models," Operations Research, INFORMS, vol. 24(2), pages 314-324, April.
    6. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    7. William H. Ruckle, 1981. "Ambushing Random Walks II: Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 108-120, February.
    8. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    9. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
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