Bayesian optimal knapsack procurement

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. The buyer’s problem is to select a subset of maximal quality. Money does not enter the buyer’s objective function, but only his constraints. Sellers quote prices strategically, inducing a knapsack game. We report the Bayesian optimal mechanism for the buyer’s problem. We find that simultaneous take‐it‐or‐leave‐it offers are interim optimal.