Simultaneous Bidding with a Fixed Charge if Any Bid is Successful

We consider the situation in which a bidder faces a group of simultaneous auctions that carry a single fixed charge, which is incurred if and only if one or more of the auctions are won. In a decision theoretic framework, we analyze the bidder's optimal strategy for three alternative formulations of the problem. If the bidder's only decision is selecting the auctions in which to bid, a simple decision rule is derived that holds regardless of the probabilities of winning. We also obtain necessary conditions for selecting the optimal bid levels. Finally, we present a single state variable dynamic programming formulation for obtaining the optimal amounts to bid in statistically independent auctions.