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

International audienceMany interactions between searching agents and their elusive targets are composedof a succession of steps, whether in the context of immune systems,predation or counterterrorism. In the simplest case, a two-step process startswith a search-and-hide phase, also called a hide-and-seek phase, followedby a round of pursuit–escape. Our aim is to link these two processes, usuallyanalysed separately and with different models, in a single game theory context.We define a matrix game in which a searcher looks at a fixed numberof discrete locations only once each searching for a hider, which can escapewith varying probabilities according to its location. The value of the game isthe overall probability of capture after k looks. The optimal search and hidestrategies 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 equallyattractive. This optimal strategy remains true as long as the number of looksis below an easily calculated threshold; however, above this threshold,the optimal position for the hider is where it has the highest probability ofescaping once spotte