We study the evolution of male and female mating strategies and mate choice for female fecundity and male fertilization ability in a system where both sexes can mate with multiple partners, and where there is variation in individual quality (i.e. in the availability of resources individuals can allocate to matings, mate choice and production of gametes). We find that when the cost of mating differs between sexes, the sex with higher cost of mating is reluctant to accept matings and is often also choosy, while the other sex accepts all matings. With equal mating costs, the evolution of mating strategies depends on the strength of female sperm limitation, so that when sperm limitation is strong, males are often reluctant and choosy, whereas females tend to accept available matings. Male reluctance evolves because a male's benefit per mating diminishes rapidly as he mates too often, hence losing out in the process of sperm competition as he spends much of his resources on mating costs rather than ejaculate production. When sperm limitation is weaker, females become more reluctant and males are more eager to mate. The model thus suggests that reversed sex roles are plausible outcomes of polyandry and limited sperm production. Implications for empirical studies of mate choice are discussed.