Advertisement

A composite game of hide and seek

  • Gordon McCormick
  • Guillermo OwenEmail author
Original Paper

Abstract

We consider a ‘manhunting’ game in which one player, the Hider, chooses one of several cells to hide and a second player, the Seeker, distributes his resources among the several cells. The cells differ in their characteristics: it may be easier to hide in some cells, or there may be a lower probability of betrayal in others, etc. The Hider’s survival probability depends on the characteristics of the cell chosen, as well as on the amount of resources which the Seeker expends in that cell. The Hider may need to carry out some activity while in his cell. If so, the activity creates a signal which can help the Seeker to locate the Hider. The Seeker must of course try to distinguish between the noise due to the activity and random “white” noise. We obtain a complete analytic solution for the case without signals. Simulation is used to develop good strategies for the case with signals.

Keywords

Search games White noise Hide-and-seek 

Supplementary material

10100_2017_516_MOESM1_ESM.docx (17 kb)
Supplementary material 1 (docx 16 KB)
10100_2017_516_MOESM2_ESM.docx (21 kb)
Supplementary material 2 (docx 21 KB)
10100_2017_516_MOESM3_ESM.docx (25 kb)
Supplementary material 3 (docx 24 KB)

References

  1. Brooks RR, Schwier J, Griffin C (2009) Markovian search games in heterogeneous spaces. IEEE Trans Syst Man Cybern B Cybern 39:626–35CrossRefGoogle Scholar
  2. Dobbie JM (1975) Search for an avoiding target. SIAM J Appl Math 28:72–86CrossRefGoogle Scholar
  3. Fokkink R, Lindelauf R (2013) The application of search games to counter terrorism studies. In: Alpern S, Fokkink R, Gasieniec L, Lindelauf R, Subrahmanian VS (eds) Search theory: a game theoretic perspective. Springer, New York, pp 543–547Google Scholar
  4. Forman JG (1977) Differential search games with a mobile hider. SIAM J Control Optim 15:841–56CrossRefGoogle Scholar
  5. Gal S (1979) Search games with a mobile and immobile hider. SIAM J Control Optim 17:99–122CrossRefGoogle Scholar
  6. Halpern B (1969) The robot and the rabbit—a pursuit problem. Am Math Mon 76:140–5Google Scholar
  7. McCormick GH, Owen G (2010) Manhunting: a simple search game. Int Game Theory Rev 12:293–308CrossRefGoogle Scholar
  8. Nakai T (1986) A sequential evasion—search game with a goal. J Oper Res Soc Jpn 29:113–21CrossRefGoogle Scholar
  9. Owen G, McCormick GH (2006) Finding a moving fugitive—a game theoretic representation of search. Comput Oper Res 35:1944–62CrossRefGoogle Scholar
  10. Thomas LC, Washburn AR (1991) Dynamic search games. Oper Res 39:415–22CrossRefGoogle Scholar
  11. Washburn AR (1980) Search evasion game in a fixed region. Oper Res 28:1290–8CrossRefGoogle Scholar

Copyright information

© © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018

Authors and Affiliations

  1. 1.Defense Analysis DepartmentNaval Postgraduate SchoolMontereyUSA
  2. 2.Department of MathematicsNaval Postgraduate SchoolMontereyUSA

Personalised recommendations