Electricity markets are becoming more integrated around the world. However, the knowledge of the effects of different auction formats on suppliers' strategies in the presence of transmission constraints and transmission costs is still very limited. In this paper, I analyze the performance of uniform and discriminatory price auctions in the presence of transmission constraints and transmission costs. When the transmission capacity is binding, the discriminatory price auction could outperform the uniform price auction, minimizing the equilibrium price and the transmission costs. Moreover, when the transmission capacity is binding, an increase in transmission costs could be pro-competitive when the auction is discriminatory, but not when the auction is uniform.