A dynamic auction for multi-object procurement under a hard budget constraint

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 select a subset of maximal quality. We propose a procurement mechanism that can be viewed as a game-theoretic extension of the greedy-split heuristic for the classic knapsack problem. The mechanism exhibits truthtelling in dominant strategies, is ex-post rational, and satisfies the hard budget constraint. Our mechanism obtains an optimal monotone pricing allocation if all items have the same quality. With different qualities, the equilibrium allocation is an optimal proportional pricing allocation.