Anecdotal, empirical, and experimental evidence suggests that offering extrinsic rewards for certain activities can reduce people's willingness to engage in those activities voluntarily. We propose a simple rationale for this 'crowding out' phenomenon, using standard economic arguments. The central idea is that the potential to earn rewards in return for an activity may create incentives to play 'hard to get' in an effort to increase those rewards. We discuss two specific contexts in which such incentives arise. In the first, refraining from the activity causes others to attach higher value to it because it becomes scarce. In the second, restraint serves to conceal the actor's intrinsic motivation. In both cases, not engaging in the activity causes others to offer larger rewards. Our theory yields the testable prediction that such effects are likely to occur when a motivated actor enjoys a sufficient degree of 'market power.'