Over the past two decades, there has been a rise in localized terrorist organizations that have seized control of geographical regions, leading to intricate spatial topological relations between areas controlled by terrorists and those populated by civilians. Given the complexity and duration of counter-terrorism operations, governments must continually adapt their strategies to defeat terrorists in diverse geographical configurations. These operations can be protracted and expensive, with numerous factors influencing their success. We develop a framework to investigate four spatial topological relations: no overlap between opposing forces, partial overlap, government-controlled regions within terrorist-held areas, and terrorist-controlled regions within government-controlled areas. We determine whether government forces should start strikes and, if so, analyze the allocation of resources between airstrikes and ground operations. Additionally, we assess the maximum acceptable level of civilian casualties resulting from mistaken airstrikes. Further, using an evolutionary game, we conduct an equilibrium analysis of disruptive technologies and strategies—such as unmanned aerial vehicles used by governments and the deployment of homemade rockets and bluffing tactics by terrorists—in long-term operations, examining their impact on government strike decisions. Our findings show that achieving complete success requires carefully chosen airstrike- or ground-oriented counter-terrorism operations based on their comparative advantages, while avoiding over-concentration or excessive averaging in resource allocation. In conclusion, our parsimonious framework and associated results contribute to informed optimal decision-making in counter-terrorism operations, taking into account the tradeoff between the strike resources and the disruptive offensive-defensive measures within various geographical relations between opposing forces.
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