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.