Abstract
This paper considers a special case of security games dealing with the protection of a large area divided in multiple cells for a given planning period. An intruder decides on which cell to attack and an agent selects a patrol route visiting multiple cells from a finite set of patrol routes such that some given operational conditions on the agent’s mobility are met. For example, the agent might be required to patrol some cells more often than others. In order to determine strategies for the agent that deal with these conditions and remain unpredictable for the intruder, this problem is modeled as a two-player zero-sum game with probabilistic constraints such that the operational conditions are met with high probability. We also introduce a variant of the basic constrained security game in which the payoff matrices change over time, to allow for the payoff that may change during the planning period.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Alpern, S., Morton, A., Papadaki, K.: Patrolling games. Operat. Res. 59(5), 1246–1257 (2011)
Brown, G., Carlyle, M., Salmeron, J., Wood, K.: Defending critical infrastructure. Interfaces 36(6), 530–544 (2006)
Charnes, A.: Constrained games and linear programming. Proc. Nat. Acad. Sci. 39(7), 639–641 (1953)
Fang, F., Stone, P., Tambe, M.: When security games go green: Designing defender strategies to prevent poaching and illegal fishing. In: IJCAI, pp. 2589–2595 (2015)
Gatti, N.: Game theoretical insights in strategic patrolling: model and algorithm in normal-form. In: ECAI, pp. 403–407 (2008)
Golany, B., Goldberg, N., Rothblum, U.G.: A two-resource allocation algorithm with an application to large-scale zero-sum defensive games. Comput. Oper. Res. 78, 218–229 (2017)
Haskell, W., Kar, D., Fang, F., Tambe, M., Cheung, S., Denicola, E.: Robust protection of fisheries with compass. In: Twenty-Sixth IAAI Conference (2014)
Lin, K.Y., Atkinson, M.P., Chung, T.H., Glazebrook, K.D.: A graph patrol problem with random attack times. Oper. Res. 61(3), 694–710 (2013)
MATLAB. version 9.1 (R2016b). The MathWorks Inc., Natick, Massachusetts (2016)
Meng, F., Zhan, J.: Two methods for solving constrained bi-matrix games. Open Cybern. Syst. J. 8, 1038–1041 (2014)
Owen, G.: Game Theory, 3rd edn. Academic Press, London (1995)
Peters, H.: Game Theory: A Multi-leveled Approach, 1st edn. Springer, Heidelberg (2008)
Ross, S.: Stochastic Processes. John Wiley & Sons Inc, New York (1996)
Semple, J.: Constrained games for evaluating organizational performance. Eur. J. Oper. Res. 96(1), 103–112 (1997)
Washburn, A., Lee, E.L.T.C.: Allocation of clearance assets in IED warfare. Nav. Res. Logistics (NRL) 58(3), 180–187 (2011)
Winston, W.L.: Operation Research, Applications and Algorithms. Brooks/Cole, Belmont (2004)
Wood, K.R.: Bilevel network interdiction models: formulations and solutions. In: Wiley Encyclopedia of Operations Research and Management Science (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Laan, C.M., Barros, A.I., Boucherie, R.J., Monsuur, H. (2017). Security Games with Probabilistic Constraints on the Agent’s Strategy. In: Rass, S., An, B., Kiekintveld, C., Fang, F., Schauer, S. (eds) Decision and Game Theory for Security. GameSec 2017. Lecture Notes in Computer Science(), vol 10575. Springer, Cham. https://doi.org/10.1007/978-3-319-68711-7_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-68711-7_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68710-0
Online ISBN: 978-3-319-68711-7
eBook Packages: Computer ScienceComputer Science (R0)