How should a guy handle a coquette's (mixed signals, hot/cold) behavior?

He can't read her mind or really know why's she's doing it. Maybe she has mixed feelings about him, maybe she's reacting to mixed feelings from him, maybe she's hoping he chases her, maybe she doesn't want to sound to eager and it's a defense mechanism, maybe she just craves control. Fact is, it often leads to frustration and confusion. I'm dealing with a girl like that, and if she's acting like that I don't see why I should put myself too far out there, when all I'm getting from her is confusion. Any ideas how a guy should play her game, and turn the game around? Just be completely honest, or play along? If I want to play, of course I can't eat it up when she decides to flirt.
How should a guy handle a coquette's (mixed signals, hot/cold) behavior?
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