Optimal bidding in sequential auctions

When a bidder's strategy in one auction will affect his competitor's behavior in subsequent auctions, bidding in a sequence of auctions can be modeled fruitfully as a multistage control process in which the control is the bidder's strategy while the state characterizes the competitors' behavior. This paper presents such a model in which the state transition represents the competitors' reaction to the bidder's strategy. Dynamic programming is used to derive the infinite horizon optimal bidding strategy. It is shown that in steady state this optimal strategy generalizes a previous result for equilibrium bidding strategy in "one-shot" auctions.