In this paper, we explore the influence of union structure and wage pricing strategies on the welfare under a mixed oligopoly which has a public firm with budget constraint. We showed that, the total utilities of the decentralized unions are higher than the utility of the centralized union under mixed duopoly if the centralized union charges a uniform wage and the productivity difference is large. The government should restrict the centralized union formed by the public and the private firm to charge discriminatory wages, and to avoid the improper use of the monopoly power of the labour union.