Ad hoc networking has received considerable attention in the research community for seamless communications without an existing infrastructure network. However, such networks are not designed with security protection in mind and they are prone to several security attacks. One such simple attack is the packet dropping attack, where a malicious node drops all data packets, while participating normally in routing information exchange. This attack is easy to deploy and can significantly reduce the throughput in ad hoc networks.In this dissertation, we study this problem through analysis and simulation. The packet dropping attack can be a result of the behavior of a selfish node or pernicious nodes that launch blackhole or a wormhole attacks. We are only interested in detecting this attack but not the causes of the attack. In this dissertation, for simple static ad hoc networks, analysis of the throughput drop due to this attack along with its improvement when mitigated are presented. A watchdog and a newly proposed "cop" detection mechanisms are studied for mitigating the throughput degradation after detection of the attack. The watchdog mechanism is a detection mechanism that has to be typically implemented in every node in the network. The cop detection mechanism is similar to the watchdog mechanism but only a few nodes opportunistically detect malicious nodes instead of all nodes performing this function. For multiple flows in static and mobile ad hoc networks, simulations are used to study and compare both mechanisms. The study shows that the cop mechanism can improve the throughput of the network while reducing the detection load and complexity for other nodes