An Attacker-Defender Resource Allocation Game with Complementary and Substituting Effects
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The United States is funding homeland security programs with large budgets (e.g., for FY 2017, 66.8 billion dollars). A number of game-theoretic defender-attacker models have been developed to study the optimal defense resource allocation strategies for the government (defender) against the strategic adversaries (attacker). However, to our best knowledge, the substituting or complementary effects between different types of defensive resources (such as human resource, land resource, and capital resource) of the government’s resource allocation have not been taken into consideration. This research fills this gap by developing a sequential game-theoretical model which focuses on the efficient resource allocation to minimize the economic losses of government from intelligent attacks, taking into account the complementary or substituting effects. The article firstly studies the best response of the attacker for each potential defense allocation and then explores how the joint effectiveness of multiple security investments influence the defender’s strategies by developing a computational model of the defensive budget allocation among potential targets. The government's decision of defensive resource allocation with regard to the potential best response of the adversary has also been illustrated using real data. The results show that the optimal resource allocation has been significantly impacted by the joint effectiveness of security investment. New insights into policy decision of how to allocate limited homeland security budget have been provided. In particular, we find that the defender is suggested to (1) defend high-valued targets with higher priority, especially when the budget is tight, (2) allocate the highly effective resource when two types of resources have a substituting effect, regardless of the budget amount, and (3) deter attacks by not only increasing the total budget, but also choosing the resources with the higher joint effectiveness, (4) release information about the substituting or complementary effects among different types of resources, to avoid the attacks on unexpected targets.