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. There are two stages. In the first one, workers in the South decide whether to move and pay the migration costs. These costs are assumed to be sunk. In the second stage, firms offer wages to the immigrant and native workers who are in the country. 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.