Abstract In most cooperatively breeding birds, individuals do not breed with their natal group members. In order to breed, they have either to disperse into another group or wait for an opposite-sex individual to join their group. In most of these species, females disperse more than males. We develop a dynamic game-theoretic model to account for this asymmetry. When males are physically larger/heavier than females, this allows them to effectively welcome female immigrants into their natal group and overcome the local females' opposition more than vice versa. The model further assumes that the dispersal decision is not confined to a restricted time window, but is rather based on acquired information and responsive to opportunities. The model predicts that (i) females disperse more than males, and (ii) females are willing to tolerate more risks in dispersal than do males. The latter prediction is supported inter alia by the fact that in many cooperatively breeding birds, females disperse at a younger age, and further away from their natal group as compared to dispersing males. Abstract In cooperatively breeding birds, the optimal upper bound of dispersal-failure risk tolerated by females (yellow-green) and males (red-blue) as a function of the other sex's upper bound, with the ESS at their intersection. The parameter a is the maximal dispersal-failure probability for females, which decreases when males are stronger and better able to welcome emigrating females into their natal group despite local females' opposition.