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Cumulative search‐evasion games

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  • James N. Eagle
  • Alan R. Washburn

Abstract

Cumulative search‐evasion games (CSEGs) are two‐person zero‐sum search‐evasion games where play proceeds throughout some specified period without interim feedback to either of the two players. Each player moves according to a preselected plan. If (Xt, Yt,) are the positions of the two players at time t, then the game's payoff is the sum over t from 1 to T of A(Xt, Yt, t). Additionally, all paths must be “connected.” That is, the finite set of positions available for a player in any time period depends on the position selected by that player in the previous time period. One player attempts to select a mixed strategy over the feasible T‐time period paths to maximize the expected payoff. The other minimizes. Two solution procedures are given. One uses the Brown‐Robinson method of fictitious play and the other linear programming. An example problem is solved using both procedures.

Suggested Citation

  • James N. Eagle & Alan R. Washburn, 1991. "Cumulative search‐evasion games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 495-510, August.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:4:p:495-510
    DOI: 10.1002/1520-6750(199108)38:43.0.CO;2-6
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Robert F. Dell & James N. Eagle & Gustavo Henrique Alves Martins & Almir Garnier Santos, 1996. "Using multiple searchers in constrained‐path, moving‐target search problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 463-480, June.
    2. Ljiljana Pavlović, 2002. "More on the search for an infiltrator," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(1), pages 1-14, February.
    3. Ryusuke Hohzaki, 2007. "Discrete search allocation game with false contacts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 46-58, February.
    4. Ryusuke Hohzaki, 2009. "A cooperative game in search theory," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 264-278, April.
    5. Ryusuke Hohzaki, 2008. "A search game taking account of attributes of searching resources," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(1), pages 76-90, February.

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