International Journal of Game Theory

, Volume 44, Issue 2, pp 347–365 | Cite as

Search games on a network with travelling and search costs



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.


Search game on a network Traveling and search costs   Immobile hider 



The authors are grateful to two anonymous reviewers and the Associate Editor for helpful comments and suggestions. This work was supported by JSPS KAKENHI Grant Number 23510177.


  1. Alpern S (2010) Search games on trees with asymmetric travel times. SIAM J Control Optim 48:5547–5563CrossRefGoogle Scholar
  2. Alpern S, Baston V, Gal S (2008) Network search games with immobile hider, without a designated searcher starting point. Int J Game Theory 37:281–302CrossRefGoogle Scholar
  3. Alpern S, Baston V, Gal S (2009) Searching symmetric networks with utilitarian-postman paths. Networks 53:392–402CrossRefGoogle Scholar
  4. Alpern S, Gal S (2003) The theory of search games and rendezvous., Kluwer international series in operations research and management sciencesKluwer, BostonGoogle Scholar
  5. Alpern S, Lidbetter T (2013) Mining coal or finding terrorists: the expanding search paradigm. Oper Res 61:265–279CrossRefGoogle Scholar
  6. Alpern S, Lidbetter T (2013) Searching a variable speed network, Math Oper Res. doi: 10.1287/moor.2013.0634
  7. Baston V, Kikuta K (2013) Search games on networks with travelling and search costs and with arbitrary searcher starting points. Networks 62:72–79CrossRefGoogle Scholar
  8. Benavent E, Corberan A, Plata I, Sachis J (2009) Min-max K-vehicles windy rural postman problem. Networks 54:216–226CrossRefGoogle Scholar
  9. Corberan A, Plata I, Sachis J (2008) The windy general routing polyhedron: a global view of many known arc routing polyhedra. SIAM J Discr Math 22:606CrossRefGoogle Scholar
  10. Dagan A, Gal S (2008) Network search games, with arbitrary searcher starting point. Networks 52:156–161CrossRefGoogle Scholar
  11. Gal S (2013) Search games: a review, Search theory: a game theoretic perspective. Springer, New YorkGoogle Scholar
  12. Kikuta K (1995) A search game with travelling cost on a tree. J Oper Res Soc Jpn 38:70–88Google Scholar
  13. Kikuta K (2004) A search game on a cyclic graph. Nav Res Logist 51:977–993CrossRefGoogle Scholar
  14. Kikuta K, Ruckle W (1994) Initial point search on weighted trees. Nav Res Logist 41:821–831CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Faculty of Mathematical StudiesUniversity of SouthamptonSouthampton UK
  2. 2.Department of Business AdministrationUniversity of HyogoKobeJapan

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