A striking but unexplained pattern in biology is the promiscuous mating behaviour in socially monogamous species. Although females commonly solicit extra-pair copulations, the adaptive reason has remained elusive. We use evolutionary modelling of breeding ecology to show that females benefit because extra-pair paternity incentivizes males to shift focus from a single brood towards the entire neighbourhood, as they are likely to have offspring there. Male-male cooperation towards public goods and dear enemy effects of reduced territorial aggression evolve from selfish interests, and lead to safer and more productive neighbourhoods. The mechanism provides adaptive explanations for the common empirical observations that females engage in extra-pair copulations, that neighbours dominate as extra-pair sires, and that extra-pair mating correlates with predation mortality and breeding density. The models predict cooperative behaviours at breeding sites where males cooperate more towards public goods than females. Where maternity certainty makes females care for offspring at home, paternity uncertainty and a potential for offspring in several broods make males invest in communal benefits and public goods. The models further predict that benefits of extra-pair mating affect whole nests or neighbourhoods, and that cuckolding males are often cuckolded themselves. Derived from ecological mechanisms, these new perspectives point towards the evolution of sociality in birds, with relevance also for mammals and primates including humans.