Extrapair paternity (EPP) has been observed in many formally monogamous species. Male pursuit of extrapair fertilizations (EPF) is explained by the advantages of having offspring that receive essential paternal care from other males. Because females are capable of exercising a degree of control over the post-copulatory sperm competition, EPP’s persistence indicates that females benefit from EPF. Thus, EPP involves cooperation between mated females and extrapair males. On the other hand, mated males exhibit a spectrum of anti-cuckolding strategies. Hence, extrapair attributes of diverse species and populations reported in the literature are particular solutions of evolutionary games involving gender-specific cuckolding/anti-cuckolding strategies. Here we use game theoretical methods to study the effect of male paternal effort conserving strategies in situations where females seek EPF for reasons of genetic compatibility and/or in pursuit of genetic diversity for their offspring. Our results indicate that in these circumstances pursuit of EPF is the only evolutionary stable female strategy. Males, on the other hand, have two, mutually exclusive, evolutionary stable strategies: males that restrict parental care regardless of their mate’s fidelity, and males that never restrict parental care. That is, when females seek EPF for reasons of fertility assurance and/or genetic diversity, the conditional male strategy—therein the male’s parental efforts are based on his certainty of paternity—loses in competition with the unconditional strategies.