I have never been in combat but I spent a couple of minutes in the boxing ring and the first thing that happens to me is I loose all peripheral vision. Ya you could "train" to help this but I always got a sort of tunnel vision.
I'm wondering if fighter pilots experience{d} the same type of thing? As I understand it it's part of the fight or flight response. I would think that this could come into play when IDing friend or foe. I didn't have that issue,I knew the other guy wasn't going to be friendly from the start..... 
It's a very interesting topic,a bit morbid but I find it fascinating.
It's actually a huge topic in aviation John. Becoming too focused on one specific thing is a highly studied problem in aviation and more than just in fights. Aviation is one of those areas where you really have to be able to simultaneously manage multiple things all at the same time and if you can't control and prioritize your focus then you're not going to be successful. For instance, maybe you've heard the maxim "aviate, navigate, then communicate?" This is drilled into your head from the very beginning and comes directly from experiences where pilots (or crews) have flown perfectly good airplanes into the ground simply because they "forgot" to fly the plane and became single-mindedly focused on some other, many times very minor, issues. The Eastern flight into the Everglades comes to mind. When landing on a CV you have a specific instrument scan (meatball, lineup, angle of attack) that you continually do to make sure you don't forget lineup or get too slow while focused on your flight path (meatball).
This ability is so overwhelmingly important in aviation that there are countless terms, maxims, and aphorisms used to remind pilots what they should be doing such as "Keep thy airspeed up, less the earth come from below and smite thee." Other terms are "instrument scan," "situational awareness," "boresighting," and "target fixation." The second and third terms come directly from situations where a pilot is so intensely focused on precisely placing his pipper on a target (for bombs or air-to-air) that he ends up flying right into his target. Generally though, they can be used to describe any situation where the pilot's ability to manage, prioritize and time-share multiple tasks breaks down in an uncontrolled fashion.
To go directly to your question yes, it's a real issue in a fight. The more intense a fight for instance, the more likely it is that the pilots aren't looking at much else except each other. In other words, their situational awareness breaks down. You have to constantly remind yourself to take a quick look around until it becomes second nature.
