We show that a firm’s profits under Cournot oligopoly can be increasing in the number of firms in the industry if wages are determined by decentralised bargaining in unionised bilateral oligopoly. The intuition for the result is that increased product market competition following an increase in the number of firms is mirrored by increased labour market rivalry which induces (profit-enhancing) wage moderation. Whether the product or labour market effect dominates depends both on the extent of union bargaining power and on the nature of union preferences. An incumbent monopolist will have an incentive to accommodate entry if the labour market effect dominates. We also show that this incentive is stronger if the incumbent anticipates that, post entry, it will be able to act as a Stackelberg leader.