In this paper, we draw the attention of biologists to a result from the economic literature, which suggests that when individuals are engaged in a communal activity of benefit to all, selection may favour cooperative sharing of resources even among non-relatives. Provided that group members all invest some resources in the public good, they should refrain from conflict over the division of these resources. The reason is that, given diminishing returns on investment in public and private goods, claiming (or ceding) a greater share of total resources only leads to the actor (or its competitors) investing more in the public good, such that the marginal costs and benefits of investment remain in balance. This cancels out any individual benefits of resource competition. We illustrate how this idea may be applied in the context of biparental care, using a sequential game in which parents first compete with one another over resources, and then choose how to allocate the resources they each obtain to care of their joint young (public good) versus their own survival and future reproductive success (private good). We show that when the two parents both invest in care to some extent, they should refrain from any conflict over the division of resources. The same effect can also support asymmetric outcomes in which one parent competes for resources and invests in care, whereas the other does not invest but refrains from competition. The fact that the caring parent gains higher fitness pay-offs at these equilibria suggests that abandoning a partner is not always to the latter's detriment, when the potential for resource competition is taken into account, but may instead be of benefit to the ‘abandoned’ mate.