According to the Lisbon Treaty the increasing cost of enforcing the European border against immigration shall be shared among the EU members. Nonetheless, the Treaty is rather vague with respect to the "appropriate measures" to adopt in order to distribute the financial burden. Members who do not share their borders with source countries have an incentive to free ride on the other countries. We study a contribution game where a northern government and a southern government minimize a loss function with respect to their national immigration target. We consider both sequential and simultaneous decisions and we show that the contribution of both governments is positive when their immigration targets are not too different. We show that total contribution is higher when decisions are simultaneous, but the conditions for both contributions to be positive are less restrictive in the sequential framework.