This paper proposes an estimation method for a repeated auction game under the presence of capacity constraints. The estimation strategy is computationally simple as it does not require solving for the equilibrium of the game. It uses a two stage approach. In the first stage the distribution of bids conditional on state variables is estimated using data on bids, bidder characteristics, and contract characteristics. In the second stage, an expression of the expected sum of future profits based on the distribution of bids is obtained, and costs are inferred based on the first order condition of optimal bids.