Autonomous Agents and Multi-Agent Systems

, Volume 28, Issue 1, pp 31–71 | Cite as

An extended study on multi-objective security games

  • Matthew Brown
  • Bo An
  • Christopher Kiekintveld
  • Fernando Ordóñez
  • Milind Tambe


The burgeoning area of security games has focused on real-world domains where security agencies protect critical infrastructure from a diverse set of adaptive adversaries. In such domains, decision makers have multiple competing objectives they must consider which may take different forms that are not readily comparable including safety, cost, and public perception. Thus, it can be difficult to know how to weigh the different objectives when deciding on a security strategy. To address the challenges of these domains, we propose a fundamentally different solution concept, multi-objective security games (MOSGs). Instead of a single optimal solution, MOSGs have a set of Pareto optimal (non-dominated) solutions referred to as the Pareto frontier, which can be generated by solving a sequence of constrained single-objective optimization problems (CSOPs). The Pareto frontier allows the decision maker to analyze the tradeoffs that exist between the multiple objectives. Our contributions include: (i) an algorithm, Iterative-ε-Constraints,, for generating the sequence of CSOPs; (ii) an exact approach for solving an mixed-integer linear program (MILP) formulation of a CSOP; (iii) heuristics that achieve speed up by exploiting the structure of security games to further constrain the MILP; (iv) an approximate approach for solving a CSOP built off those same heuristics, increasing the scalability of our approach with quality guarantees. Additional contributions of this paper include proofs on the level of approximation, detailed experimental evaluation of the proposed approaches and heuristics, as well as a discussion on techniques for visualizing the Pareto frontier.


Game theory Security Multi-objective optimization 


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Matthew Brown
    • 1
  • Bo An
    • 1
    • 2
  • Christopher Kiekintveld
    • 3
  • Fernando Ordóñez
    • 4
  • Milind Tambe
    • 1
  1. 1.University of Southern CaliforniaLos AngelesUSA
  2. 2.Chinese Academy of SciencesBeijingChina
  3. 3.University of Texas at El PasoEl PasoUSA
  4. 4.Universidad de ChileSantiagoChile

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