Using an online experiment with 5,762 US participants, we investigate whether individuals who seek competition face inaccurate perceptions of their behaviors and personality and whether women are held to different standards than men. We find that evaluators perceive competitive women as less social, more career-oriented, and less (stereotypically) feminine and more (stereotypically) masculine than they actually are or state to be. However, competitive men face similarly inaccurate beliefs and hence belief accuracy does not differ for men and women. Nevertheless, our findings point to social penalties that competitive women may experience -- not for seeking competition itself (which is socially accepted), but because the behaviors associated with seeking competition violate gender-specific norms. Meanwhile, men encounter a double-edged sword: while seeking competition earns them esteem, both, behaviors associated with seeking and avoiding competition can lead to social penalties.