Reproductive genetic technologies (RGTs) allow parents to decide whether their future children will have or lack certain genetic predispositions. A popular model that has been proposed for regulating access to RGTs is the ‘genetic supermarket’. In the genetic supermarket, parents are free to make decisions about which genes to select for their children with little state interference. One possible consequence of the genetic supermarket is that collective action problems will arise: if rational individuals use the genetic supermarket in isolation from one another, this may have a negative effect on society as a whole, including future generations. In this article we argue that RGTs targeting height, innate immunity, and certain cognitive traits could lead to collective action problems. We then discuss whether this risk could in principle justify state intervention in the genetic supermarket. We argue that there is a plausible prima facie case for the view that such state intervention would be justified and respond to a number of arguments that might be adduced against that view.