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Search games on a network with travelling and search costs

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  • Vic Baston
  • Kensaku Kikuta

Abstract

The authors analyse two-person zero-sum search games in which play takes place on a network and in discrete time. The hider first chooses a node and remains there for the duration of the game. The searcher then chooses a node and searches there. At each subsequent time instant the searcher moves from the node he occupies to an adjacent node and decides whether or not to search it. Play terminates when the searcher is at the node chosen by the hider and searches there. The searcher incurs costs in moving from one node to another and also when a node is searched. The searcher wants to minimize the costs of finding the hider and the hider wants to maximize them. The paper has two main strands. The first investigates these games on directed, not necessarily strongly connected, networks; previous work has tended to concentrate on undirected networks. The second complements previous work on undirected networks by obtaining results for the case when the search cost is the same for all nodes. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Vic Baston & Kensaku Kikuta, 2015. "Search games on a network with travelling and search costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 347-365, May.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:2:p:347-365
    DOI: 10.1007/s00182-014-0432-z
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    References listed on IDEAS

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    1. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    2. Kensaku Kikuta & William H. Ruckle, 1994. "Initial point search on weighted trees," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 821-831, October.
    3. Steve Alpern & Vic Baston & Shmuel Gal, 2008. "Network search games with immobile hider, without a designated searcher starting point," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 281-302, June.
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    Citations

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    Cited by:

    1. Steve Alpern, 2017. "Hide-and-Seek Games on a Network, Using Combinatorial Search Paths," Operations Research, INFORMS, vol. 65(5), pages 1207-1214, October.
    2. Yolmeh, Abdolmajid & Baykal-Gürsoy, Melike, 2021. "Weighted network search games with multiple hidden objects and multiple search teams," European Journal of Operational Research, Elsevier, vol. 289(1), pages 338-349.
    3. Lisa Hellerstein & Thomas Lidbetter & Daniel Pirutinsky, 2019. "Solving Zero-Sum Games Using Best-Response Oracles with Applications to Search Games," Operations Research, INFORMS, vol. 67(3), pages 731-743, May.
    4. Steve Alpern & Thomas Lidbetter, 2019. "Approximate solutions for expanding search games on general networks," Annals of Operations Research, Springer, vol. 275(2), pages 259-279, April.
    5. Lidbetter, Thomas, 2020. "Search and rescue in the face of uncertain threats," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1153-1160.
    6. Baston, Vic & Kikuta, Kensaku, 2019. "A search problem on a bipartite network," European Journal of Operational Research, Elsevier, vol. 277(1), pages 227-237.
    7. Lidbetter, Thomas, 2017. "On the approximation ratio of the Random Chinese Postman Tour for network search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 782-788.

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