Individual competitiveness is a personality trait of high importance. While substantial differences between individuals have been documented, the sources of this heterogeneity are not well understood. To contribute to this issue we conduct an incentivized field study with pre-school children. We assess the children’s willingness to compete and relate the inclinations to ambitions and preferences of their parents. Parents’ ambitions concerning their children’s success in professional life predict their children’s competitiveness. In particular, children of highly ambitious parents tend to enter competition even if their chances to win are low. High ambitions are related to a relatively low socioeconomic background.