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The authors present a new dynamic auction for procurement problems where payments are bounded by a hard budget constraint and money does not enter the procurer's objective function. A budget-constrained buyer wants to purchase items from a shortlisted set. Items are differentiated by observable quality and sellers have private reserve prices for their items. Sellers quote prices strategically, inducing a knapsack game. The buyer's problem is to procure a subset of maximal quality. They study a procurement auction that can be viewed as a game-theoretic extension of the greedy-split heuristic for the classic knapsack problem. The auction exhibits truth telling in dominant strategies, is ex-post rational, and satisfies the hard budget constraint.
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