This paper investigates game theory applications in security.
This dissertation studies the applications of game theory in determining protection strategies for various infrastructures. The first part considers the resource allocation game models, and in the second part, they study patrolling and search games. The authors study one-shot security games under uncertainty about target valuations and propose a model in which both players use a robust approach to contend with the uncertainty of target valuations. They show that the Nash equilibrium for this model is of threshold type and develop closed-form solutions to characterize the equilibrium point. The authors apply their model to a real case of assigning funds for security to 10 urban areas in the U.S., developing a two-stage game model. The results reveal that an increase in defense investments on a target site decreases the probability of both defending and attacking that target. The authors also apply the proposed model to a real case, demonstrating that the attacker's penalty from a failed attack is an important factor in determining the defender's optimal distribution of investments and defense probabilities. The researchers also investigate the overarching protection options in the resource allocation models, showing that the proposed model is a convex optimization problem that can be solved to optimality in polynomial time and that the overall country-level resource allocation problem can be decomposed into smaller city-level subproblems, resulting in a more efficient algorithm. The authors propose new models with time-dependent node values and node-based attack times and solve these models numerically using algorithms, applying these algorithms to a real case.