Hyper-competitiveness can also lead to rather humorous situations. I've noticed this when biking to and from one of my offices away from the office (i.e., various coffee shops in the area). When doing so, I usually take the Los Gatos Creek Trail, and I apparently bike fairly close to the "flow of traffic." That is, I do not pass or am passed by too many other bike riders. The exception to this are bikers on road bikes. Their bikes are much lighter, have thinner tires, and typically use higher quality derailleurs. Thus, they are far more likely to pass me than I am to pass them.
Interestingly, on those few occasions when I do pass a biker on a road bike, many of them seem to take offense, and as soon as they realize what has happened, they speed up and pass by me. Once they do so, however, it's not unusual for them to slow down, which means I eventually pass them again, leading them speed up once again so they can pass me. Recently, I caught and passed a gentlemen on a road bike, and predictably he soon sped up and caught up with me. He, however, didn't try to pass. Instead, he slid in close behind me (known as drafting) and stayed their for several miles. No doubt he rationalized his behavior as smart biking, but I'm pretty sure he just doesn't like getting passed.