Crowdsourcing offers unprecedented potential for solving tasks efficiently by tapping into the skills of large groups of people. A salient feature of crowdsourcing---its openness of entry---makes it vulnerable to malicious behavior. Such behavior took place in a number of recent popular crowdsourcing competitions. We provide game-theoretic analysis of a fundamental tradeoff between the potential for increased productivity and the possibility of being set back by malicious behavior. Our results show that in crowdsourcing competitions malicious behavior is the norm, not the anomaly---a result contrary to the conventional wisdom in the area. Counterintuitively, making the attacks more costly does not deter them but leads to a less desirable outcome. These findings have cautionary implications for the design of crowdsourcing competitions.