In frequency-dependent games, strategy choice may be innate or learned. While experimental evidence in the producer-scrounger game suggests that learned strategy choice may be common, a recent theoretical analysis demonstrated that learning by only some individuals prevents learning from evolving in others. Here, however, we model learning explicitly, and demonstrate that learning can easily evolve in the whole population. We used an agent-based evolutionary simulation of the producer-scrounger game to test the success of two general learning rules for strategy choice. We found that learning was eventually acquired by all individuals under a sufficient degree of environmental fluctuation, and when players were phenotypically asymmetric. In the absence of sufficient environmental change or phenotypic asymmetries, the correct target for learning seems to be confounded by game dynamics, and innate strategy choice is likely to be fixed in the population. The results demonstrate that under biologically plausible conditions, learning can easily evolve in the whole population and that phenotypic asymmetry is important for the evolution of learned strategy choice, especially in a stable or mildly changing environment.