We investigate individual heterogeneity in the tendency to under-respond to feedback ("conservatism") and to respond more strongly to positive compared to negative feedback ("asymmetry"). We elicit beliefs about relative performance after repeated rounds of feedback across a series of cognitive tests. Relative to a Bayesian benchmark, we find that subjects update on average conservatively but not asymmetrically. We define individual measures of conservatism and asymmetry relative to the average subject, and show that these measures explain an important part of the variation in beliefs and competition entry decisions. Relative conservatism is correlated across tasks and predicts competition entry both independently of beliefs and by influencing beliefs, suggesting it can be considered a personal trait. Relative asymmetry is less stable across tasks, but predicts competition entry by increasing self-confidence. Ego-relevance of the task correlates with relative conservatism but not relative asymmetry.