What's the fun in playing staring games?

First of all, some context: I'm very quiet and hard to approach. If some guy starts smiling at me, and I'm not interested, I just ignore it, because I hate turning people down. So guys often smile at me but hardly get to talk to me.

A lot of times, these guys will instead start constantly smiling or staring at me whenever they see me. It gets to the point where they notice me the instant I walk into a crowded room. Sometimes it's creepy, but not most of the time. They keep this up for months or years. It turns into an endless, annoying game.

Can anyone tell me what the fun of this is? I never pay attention to them, so they don't get attention out of it. They just seem to put so much effort into it, it's obsessive. Right now, I'm about to be rid of a smart, outgoing musician who's been doing this to me since fall 2010 (he's finally graduating). I'm trying to make sense of it. Are there people who enjoy being weirdly obsessed with someone else instead of actually dating?
What's the fun in playing staring games?
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