Supplier selection is one of the most critical decisions in a supply chain. While good suppliers can contribute to the supply chain's overall performance, incorrect selection can drive the whole supply chain into disarray. In this paper, we focus on the problem of supplier selection in a manufacturing firm. We allow each supplier to compete with each other to be selected by the buyer for procurement. The competition is modeled in an auction framework as a bidding process where a supplier cannot observe immediate actions of other suppliers but has complete knowledge of their previous actions. We allow a supplier to use this knowledge in guessing other suppliers future actions and bid accordingly. Our model enables repeated games, which can be assumed to be more flexible compared to most game theory applications in the supplier selection literature. Reinforcement learning and fictitious play are used in the auction framework to implement repeated games.