Actually, the first drone (U.S. Predator MQ-1) vs. manned fighter jet (Iraqi MiG-25) dogfight happened in 2002. At the time, the U.S. was using Predators to bait Iraqi fighters and then run (Israel had successfully done something similar against Egypt and Syria in the early 1980s using F-4s as bait). The MiG engaged the Predator, and the Predator, which was armed with Stinger missiles, did not run. Both both fired missiles at each other. The Predator missed; the MiG didn't. You can see a video of the dogfight here http://www.liveleak.com/view?i=76a_1173456397 [CBS video hosted on liveleak.com], and read about it here https://en.wikipedia.org/wiki/Mikoyan-Gurevich_MiG-25#Persian_Gulf_War [wikipedia.org].
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Actually, the first drone (U.S. Predator MQ-1) vs. manned fighter jet (Iraqi MiG-25) dogfight happened in 2002. At the time, the U.S. was using Predators to bait Iraqi fighters and then run (Israel had successfully done something similar against Egypt and Syria in the early 1980s using F-4s as bait). The MiG engaged the Predator, and the Predator, which was armed with Stinger missiles, did not run. Both both fired missiles at each other. The Predator missed; the MiG didn't. You can see a video of the dogfight here http://www.liveleak.com/view?i=76a_1173456397 [CBS video hosted on liveleak.com], and read about it here https://en.wikipedia.org/wiki/Mikoyan-Gurevich_MiG-25#Persian_Gulf_War [wikipedia.org].