A sizable amount of U.S. federal government spending is made via procurement through full and open competition. The procuring officers have a broad range of discretion in designing the contracts and selecting winners. To evaluate whether the winner of such competition is selected based on bidders' brand, sustainability, and political ideology, this paper develops and structurally estimates an auction game. Firms with hidden efficiency types and multi-dimensional characteristics participate in an auction designed by the government. We analytically characterize the optimal mechanism design to reveal the role of competition and the role of the pecuniary and non-pecuniary factors in determining procurement outcomes. By structurally estimating the model using detailed contract-level data, we show that bidders' brand, sustainability, and political ideology play significant roles in procurement and the government is willing to pay a significant premium for these attributes, though their relative importance exhibits large heterogeneity across industries.