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Continuous Accumulation Games in Continuous Regions

Author

Listed:
  • W. H. Ruckle

    (Clemson University)

  • K. Kikuta

    (Kobe University of Commerce)

Abstract

In a continuous accumulation game on a continuous region, a Hider distributes material over a continuous region at each instant of discrete time, and a Seeker examines the region. If the Seeker locates any of the material hidden, the Seeker confiscates it. The goal of the Hider is to accumulate a certain amount of material before a given time, and the goal of the Seeker is to prevent this. In previous works, we have studied accumulation games involving discrete objects and continuous material over discrete locations. The issues raised when the region is continuous are substantially different. In this paper, we study accumulation of continuous material over two types of continuous regions: the interval and the circle.

Suggested Citation

  • W. H. Ruckle & K. Kikuta, 2000. "Continuous Accumulation Games in Continuous Regions," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 581-601, September.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:3:d:10.1023_a:1004609529766
    DOI: 10.1023/A:1004609529766
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    Citations

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    Cited by:

    1. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.
    2. Kensaku Kikuta & William H. Ruckle, 2002. "Continuous accumulation games on discrete locations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(1), pages 60-77, February.
    3. Steve Alpern & Robbert Fokkink & Christos Pelekis, 2012. "A Proof of the Kikuta–Ruckle Conjecture on Cyclic Caching of Resources," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 650-661, June.
    4. Oléron Evans, Thomas P. & Bishop, Steven R., 2013. "Static search games played over graphs and general metric spaces," European Journal of Operational Research, Elsevier, vol. 231(3), pages 667-689.
    5. Endre Csóka & Thomas Lidbetter, 2016. "The solution to an open problem for a caching game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(1), pages 23-31, February.

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