One prominent security threat that targets unmanned aerial vehicles (UAVs) is the capture via GPS spoofing in which an attacker manipulates a UAVs global positioning system (GPS) signals in order to capture it. Given the anticipated widespread deployment of UAVs for various purposes, it is imperative to develop new security solutions against such attacks. In this paper, a mathematical framework is introduced for analyzing and mitigating the effects of GPS spoofing attacks on UAVs. In particular, system dynamics are used to model the optimal routes that the UAVs will adopt to reach their destinations. The GPS spoofers effect on each UAVs route is also captured by the model. To this end, the spoofers optimal imposed locations on the UAVs, are analytically derived; allowing the UAVs to predict their traveling routes under attack. Then, a countermeasure mechanism is developed to mitigate the effect of the GPS spoofing attack. The countermeasure is built on the premise of cooperative localization, in which a UAV can determine its location using nearby UAVs instead of the possibly compromised GPS locations. To better utilize the proposed defense mechanism, a dynamic Stackelberg game is formulated to model the interactions between a GPS spoofer and a drone operator. In particular, the drone operator acts as the leader that determines its optimal strategy in light of the spoofers expected response strategy. The equilibrium strategies of the game are then analytically characterized and studied through a novel proposed algorithm. Simulation results show that, when combined with the Stackelberg strategies, the proposed defense mechanism will outperform baseline strategy selection techniques in terms of reducing the possibility of UAV capture
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