Security Games with Restricted Strategies: An Approximate Dynamic Programming Approach

Corine Maartje Laan, Ana Isabel Barros, Richard Boucherie, Herman Monsuur

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review


In this chapter we consider a security game between an agent and an intruder to find optimal strategies for patrolling against illegal fishery. When patrolling large areas that consist of multiple cells, several aspects have to be taken into account. First, the current risk of the cells has to be considered such that cells with high risk are visited more often. Moreover, it is important to be unpredictable in order to increase the patrolling effectiveness countering illegal fishery. Finally, patrolling strategies have to be chosen in such a manner that they satisfy given operational requirements. For example, the agent might be required to patrol some cells more often than others imposing extra restrictions on the agent strategies. In this chapter, we develop a dynamic variant of the security game with restrictions on the agent’s strategy so that all these requirements are taken into account. We model this game as a stochastic game with a final penalty to ensure that the operational requirements are met. In this way, strategies are formed that both consider past actions and expected future risk levels. Due to the curse of dimensionality, these stochastic games cannot be solved for large scale instances. We develop an approximate dynamic programming algorithm to find approximate solutions.
Original languageEnglish
Title of host publicationNL ARMS Netherlands Annual Review of Military Studies 2018
Subtitle of host publicationCoastal Border Control: From Data and Tasks to Deployment and Law Enforcement
EditorsHerman Monsuur
Place of PublicationThe Hague
PublisherT.M.C. Asser Press
Number of pages21
ISBN (Electronic)978-94-6265-246-0
ISBN (Print)978-94-6265-246-0_9
Publication statusPublished - 13 Jul 2018

Publication series

NameNL ARMS : Netherlands Annual Review of Military Studies
PublisherT.M.C. Asser Press
ISSN (Print)1387-8050
ISSN (Electronic)2452-235X


  • Stochastic games
  • Security
  • Patrolling
  • Restricted strategies
  • Approximate dynamic programming
  • Aggregation


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