Succession of hide-seek and pursuit-evasion at heterogeneous locations

Shmuel Gal, Jérôme Casas

Research output: Contribution to journalArticlepeer-review

Abstract

Many interactions between searching agents and their elusive targets are composed of a succession of steps, whether in the context of immune systems, predation or counterterrorism. In the simplest case, a two-step process starts with a search-and-hide phase, also called a hide-and-seek phase, followed by a round of pursuit-escape. Our aim is to link these two processes, usually analysed separately and with different models, in a single game theory context. We define a matrix game in which a searcher looks at a fixed number of discrete locations only once each searching for a hider, which can escape with varying probabilities according to its location. The value of the game is the overall probability of capture after k looks. The optimal search and hide strategies are described. If a searcher looks only once into any of the locations, an optimal hider chooses it's hiding place so as to make all locations equally attractive. This optimal strategy remains true as long as the number of looks is below an easily calculated threshold; however, above this threshold, the optimal position for the hider is where it has the highest probability of escaping once spotted.

Original languageEnglish
Article number20140062
JournalJournal of the Royal Society Interface
Volume11
Issue number94
DOIs
StatePublished - 6 May 2014

Keywords

  • Behavioural ecology
  • Foraging
  • Game theory
  • Optimization
  • Search games

ASJC Scopus subject areas

  • Bioengineering
  • Biophysics
  • Biochemistry
  • Biotechnology
  • Biomedical Engineering
  • Biomaterials

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