Search game in a rectangle

  • A. Yu. Garnaev
Contributed Papers

Abstract

We consider a search game in which the searcher (player S) moves along a continuous trajectory in a rectangleQ. The velocity vectogram of player S is a rhombus-type set. In this paper, we construct the strategies of both players which make it possible to find the asymptotic value of the game in the case of small discovery radius.

Key Words

Search games princess and monster games optimal strategies value of the game 

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References

  1. 1.
    Isaacs, R.,Differential Games, John Wiley aand Sons, New York, New York, 1965.Google Scholar
  2. 2.
    Gal, S.,Search Games with Mobile and Immobile Hider, SIAM Journal on Control and Optimization, Vol. 17, pp. 99–122, 1979.Google Scholar
  3. 3.
    Zelikin, M. I.,On a Differential Game with Incomplete Information, Soviet Mathematics—Doklady, Vol. 13, pp. 228–231, 1972.Google Scholar
  4. 4.
    Alpern, S.,The Search Game with Mobile Hider on the Circle, Differential Games and Control Theory, Edited by E. O. Roxin, T. P. Liu, and R. L. Sternberg, Marcel Dekker, New York, New York, pp. 181–200, 1974.Google Scholar
  5. 5.
    Gal, S.,Search Games, Academic Press, New York, New York, 1980.Google Scholar
  6. 6.
    Fitzgerald, C. G.,The Princess and Monster Differential Game, SIAM Journal on Control and Optimization, Vol. 17, pp. 700–712, 1979.Google Scholar
  7. 7.
    Alpern, S., andAsic, M.,Ambush Strategies in Search Games on Graphs, SIAM Journal on Control and Optimization, Vol. 17, pp. 66–75, 1986.Google Scholar
  8. 8.
    Garnaev, A. YU.,Solving the Search Problem in a Domain, Vestnik Leningrad University, Mathematics, Vol. 20, pp. 9–17, 1987.Google Scholar
  9. 9.
    Lalley, S., andRobbins, H.,Stochastic Search in a Convex Region, Probability Theory and Related Fields, Vol. 77, pp. 99–116, 1988.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • A. Yu. Garnaev
    • 1
  1. 1.Department of Computational MathematicsLeningrad Civil Engineering InstituteLeningradUSSR

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