PurposeThe authors provide a novel interpretation of the relationship between skill demand and labour market concentration based on the training rationale.Design/methodology/approachThe authors use a novel data set on Italian online job vacancies during 2013–2018 to analyse the relationship between labour market concentration and employers' skill demand. The authors construct measures of market concentration and skill intensity in the local labour market. The authors regress the measures of skill demand on market concentration, controlling for sector, occupations and other features of the labour market. The authors also use the Hausman–Nevo instrument for market concentration.FindingsThe authors show that employers in a highly concentrated labour market demand competencies associated with the ability of workers to learn faster (e.g. social skills) rather than actual knowledge. They also require less experience but higher education. These results are consistent with the hypothesis that employers in more concentrated labour markets are more prone to train their employees. Instead of looking for workers who already have job-specific skills, they look for workers who can acquire them faster and efficiently. The authors provide a theoretical framework within which to analyse these aspects as well as providing a test for the relevant hypotheses.Practical implicationsIn addition to cross-countries differences in labour market regulations, the authors' findings suggest that policy authorities should consider the local labour market structure when studying workforce development programmes aimed at bridging the skill gap of displaced workers. Moreover, the authors show that market concentration can have relevant implications for human resource (HR) managers by affecting their recruitment behaviour through the demand for skills. In fact, concentrated markets tend to favour firms' collusion and anti-competitive behaviour that could strongly affect HR management practices.Originality/valueThe authors' paper innovates on the literature in a number of ways. First, the authors provide evidence of local labour market concentration in Italy. Second, the authors provide evidence of skill demand at the local level using a detailed skill taxonomy that goes beyond the classical distinction between high and low skills. Third, and most importantly, the authors provide evidence of the relationship between skill demand and labour market concentration. By analysing detailed skills and competencies, the authors take one step beyond understanding the features of labour demand in monopsonistic markets.