We consider a three-stage game to examine how market integration affects firms' incentives to provide general worker training. In stage 1, firms invest in productivity-enhancing training. In stage 2, they can make wage offers for each others' workers. Finally, Cournot competition takes place. When two product markets become integrated, that is, replaced by a market with greater demand and more firms, training by each firm increases, provided the two markets are initially sufficiently concentrated. When barriers between less concentrated markets are eliminated, training is reduced. Integration increases welfare if it does not reduce training. However, for large parameter regions, welfare decreases if integration reduces training. We also show that opening product markets to countries with publicly funded training or cheap, low-skilled labor can threaten apprenticeship systems.