We consider a model of international migration where skills of workers are imperfectly observed by firms in the host country and where information asymmetries are more severe for immigrants than for natives. Because of imperfect information, firms statistically discriminate high-skilled migrants by paying them at their expected productivity. The decision of whether to migrate or not depends on the proportion of high-skilled workers among the migrants. The migration game exhibits strategic complementarities, which, because of standard coordination problems, lead to multiple equilibria. We characterize them and examine how international migration affects the income of individuals in sending and receiving countries, and of migrants themselves.We also analyze under which conditions there is positive or negative self-selection of migrants.