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Searching for a mobile hider in a directed bipartite graph

Author

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  • Ashkenazi-Golan, Galit
  • Flesch, János
  • Schröder, Marc

Abstract

We examine a dynamic search game played between two players, the hider and the searcher. The game takes place in a directed bipartite graph, consisting of two partitions A and B, such that all arcs go from vertices in A to vertices in B. The hider chooses an initial vertex and hides there, and at any period, if she is in a vertex in partition A, she has the option to stay or to travel along one of the outgoing arcs to a vertex in B. The searcher at each period chooses an arbitrary vertex of the graph, and if the hider is there, then the hider is found and the game ends. The hider does not observe which vertex is searched by the searcher. The searcher’s goal is to minimize the expected search time, whereas the hider’s goal is to maximize it. One interpretation of the game is that a rescue team searches possible locations of an injured person on two sides of a river, while considering the worse-case scenario.

Suggested Citation

  • Ashkenazi-Golan, Galit & Flesch, János & Schröder, Marc, 2026. "Searching for a mobile hider in a directed bipartite graph," European Journal of Operational Research, Elsevier, vol. 335(2), pages 648-660.
    • Handle: RePEc:eee:ejores:v:335:y:2026:i:2:p:648-660
    DOI: 10.1016/j.ejor.2026.05.013
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