On bidding for a fixed number of items in a sequence of auctions

We consider the problem of a firm ( the buyer ) that must acquire a fixed number (L) of items. The buyer can acquire these items either at a fixed buy-it-now price in the open market or by participating in a sequence of N \u3e L auctions. The objective of the buyer is to minimize his expected total cost for acquiring all L items. We model this problem as a Markov Decision Process and establish monotonicity properties for the optimal value function and the optimal bidding strategies. © 2012 Elsevier B.V. All rights reserved