Whether competition forces firms toward efficient behaviour is an open question. We consider a duopoly with firms run by managers and affected by adverse selection on costs. In contrast to recent literature, we point out that, to have a genuine effect on firm X-inefficiency, competition must change managerial incentives. By introducing the availability of some signal on the rivals' behaviour we show that, if costs are correlated, the contractual use of that signal can render private managerial information uninfluential. This result stresses the informational role of the market and suggests scope for future work.