A dynamic two-country labour matching economy is presented. Workers decide whether to search in their native country or look for a job abroad (bearing an additional cost). The number of vacancies posted by firms in each country depends on the average characteristics of the workers searching inside that country. Wages are determined in an individual Nash bargain. We show the existence of multiple steady-state equilibria: one no-migration equilibrium and two migration equilibria. The multiplicity of equilibria is due to a self-fulfilling prophecy phenomenon linking average wages and incentives to migrate. The equilibria are Pareto-ranked, with migration-equilibria dominating no-migration.