We present a model where the interaction between competition at school, industrial structure and labour market outcomes is characterised by the concept of Nash decentralised equilibrium. We show that the presence of spillovers and strategic complementarities could generate multiple equilibria. In one equilibrium, a competitive schooling system induces individuals to accumulate basic academic skills, large firms hire mainly new school graduates and there is limited labour turnover. In another equilibrium, schooling is less competitive and individuals focus more on idiosyncratic skills, large firms hire mainly experienced workers and labour turnover is important. We argue in the paper that the main features of each equilibrium are consistent with key stylised facts of the Italian and the Japanese labour markets.