Investigating the evolution of consistent between-individual behavioral differences necessitates to explain the emergence of within-individual consistency. Relying on a recent mathematical model, we here test the prediction that the emergence of differences in within-individual consistency is related to the sequential access to resources in a frequency-dependent foraging game. To this end we used flocks of zebra finches (Taeniopygia guttata) engaged in a producer-scrounger foraging game. Tactic investment (i.e. the proportion of hops with the head down) significantly predicted successful tactic use (i.e. the proportion of seeds produced). In support of predictions, we found that individuals that arrived first at a foraging area were more consistent in both their investment into and their use of the producer tactic. Also, birds in higher body condition were less consistent in their producer tactic use. These results provide the first evidence that variation in behavioral consistency can emerge through the sequential access to resources in a frequency-dependent game. They also highlight a potential physiological cost of behavioral flexibility. Our findings suggest an explanation for the link between personality traits and social information use.