We experimentally investigate the determinants of overconfidence and test the hypothesis, advanced by Robert Trivers, that overconfidence serves to more effectively persuade or deceive others. After performing a cognitively challenging task, half of our subjects are informed about the possibility of earning money by convincing others of their high relative performance in a structured face-to-face interaction. Privately elicited beliefs show that informed participants are 50% more overconfident than those in a control condition, and are less responsive to objective feedback on their performance. Using random variation in confidence generated by our feedback mechanism, we find that increased confidence indeed causes higher evaluations in the ensuing interactions, unless the evaluators have been explicitly instructed to watch out for lies. These results support the idea that confidence is a strategic variable in human interaction.