How to allocate research (and other) subsidies

A budget-constrained buyer wants to purchase items from a short-listed 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 derive the Bayesian optimal mechanism for the buyer's problem. We find that simultaneous take-it-or-leave-it offers are optimal. Hence, somewhat surprisingly, ex-postcompetition is not required to implement optimality. Finally, we discuss the problem in a detail free setting.