In many species, individuals express phenotypic characteristics that enhance their competitiveness, that is, the ability to acquire resources in competition with others. Moreover, the degree of competitiveness varies considerably across individuals and in time. By means of an evolutionary model, we provide an explanation for this finding. We make the assumption that investment into competitiveness enhances the probability to acquire a high-quality resource, but at the same time reduces the ability of exploiting acquired resources with maximal efficiency. The model reveals that under a broad range of conditions competitiveness either converges to a polymorphic state, where individuals differing in competitive ability stably coexist, or is subject to perpetual transitions between periods of high and low competitiveness. The dynamics becomes even more complex if females can evolve preferences for (or against) competitive males. In extreme cases, such preferences can even drive the population to extinction.