Multimedia Tools and Applications

, Volume 77, Issue 9, pp 10961–10977 | Cite as

A double oracle algorithm for allocating resources on nodes in graph-based security games

  • Zhou Yang
  • Junwu Zhu
  • Ling Teng
  • Jiajie Xu
  • Zeyu Zhu


In the graph-based security game, the defender allocates security resources strategically to protect targets against the adversary. In this paper, firstly, we come up with a new double oracle algorithm for scheduling resources optimally on nodes in graph-based security games. The police scattered on the street can only detect those terrorists on that street, while the police at the intersection place can detect all the terriorists on all the streets crisscrossing the intersection. Secondly, in real world situation, even the police meets the criminals at the same place, criminals still could escape. To match the real world situation, we define a parameter called detection probability, representing the chance the attacker is caught when they are checked by the defenders. Thirdly, we design a double oracle algorithm to find the equilibrium. But the computational complexity of best response oracles are extremely high. We design greedy algorithms and combine them with best response oracles to improve the algorithm efficiency without loss of correctness.


Game theory Double oracle Minimax equilibria Distributed artificial intelligence Mixed integer linear programming 



Project supported by the National Nature Science Foundation of China (Grant No.61170201, No.61070133, No.61472344), Six talent peaks project in Jiangsu Province (Grant No.2011– DZXX–032), Jiangsu Science and Technology Project (Grant No. BY2015061-06, BY2015061-08), Yangzhou Science and Technology Project (Grant No. SXT20140048, SXT20150014, SXT201510013), Natural Science and Technology Project (Grant No. SXT20140048, SXT20150014, SXT201510013), Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No.14KJB520041), Jiangsu Student’s Platform for Innovation and Entrepreneurship Training Program(Grant No.201711117017Z).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Zhou Yang
    • 1
  • Junwu Zhu
    • 1
  • Ling Teng
    • 1
  • Jiajie Xu
    • 1
  • Zeyu Zhu
    • 1
  1. 1.Yangzhou UniversityYangzhouChina

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