We present a dynamic two-country labour matching economy. Workers decide whether to search in their native country (paying a small cost) or to look for a job abroad (bearing an additional cost). Firms choose the number of vacancies they post in each country according to the average workers' characteristics inside it. Wages are determined in an individual Nash bargaining. We show the existence of multiple steady-state equilibria: a no-migration equilibrium and two migration equilibria. The multiplicity of equilibria comes from a self-fulfilling prophecy phenomenon linking labour demand and incentives to migration. The equilibria are Pareto-ranked, with migration-equilibria dominating no-migration.