Methods Development for Optimal Defense against Adaptive Adversaries -- Quantification of Uncertain Preferences and Development of Computational Approaches.

摘要

This dissertation extends game-theoretic models for homeland security in three ways, all motivated by the desire to make game theory ready for use in real-world decisions. First, we introduce a simple elicitation process where subject-matter experts can provide only ordinal judgments of the attractiveness of potential targets, and the adversary preferences among targets are assumed to involve multiple attributes such as fatalities, property loss, and symbolic value. Probabilistic inversion (PI) or Bayesian density estimation (BDE) is then used to derive probability distributions representing both defender uncertainty about adversary weights on the various attributes, and also defender ignorance about unobserved attributes that may be important to the adversary, but have not yet been identified by the defender. This work also makes methodological contributions to expert elicitation in general, especially by the use of unobserved attributes to ensure the existence of feasible solutions in PI, and by elucidating the relationship between PI and BDE when applied to preference rankings.;Next, we fill a gap in the literature of game-theoretic models for homeland security by explicitly considering adversary capabilities in addition to just intent, since intelligence experts generally believe that adversary capabilities are at least as important as intent. We use contest success functions from economics to capture the extent to which the success of an attack is attributable to adversary capabilities and defender investment, rather than pure luck. Moreover, our model allows the effectiveness of adversary capabilities to differ across targets (e.g., civilian versus military targets) and attack modes (e.g., using improvised explosive devices versus nuclear weapons).;Finally, we identify and evaluate computational tools to solve for equilibrium (optimal) defensive strategies in problems of realistic size and complexity. Our proposed game with defender uncertainty about adversary characteristics is formulated as a two-stage stochastic programming problem with binary recourse, and solved using approaches based on sample-average approximation (SAA). In particular, we demonstrate that our case satisfies the conditions for convergence of SAA, and investigate two categories of state-of-the-art optimization algorithms (one based on mixed-integer nonlinear programming, and the other based on derivative-free global optimization).