Optimal Bidding in Sequential Auctions

Abstract

A bidder's strategy in one auction may affect his competitors' behavior in subsequent auctions. When this occurs, bidding in a sequence of auctions can be modeled fruitfully as a multistage control process. This paper presents such a model. In it the control is the bidder's strategy, the state characterizes the competitors' behavior and the state transition represents the competitors' reaction to the bidder's strategy. Dynamic programming is used to derive the infinite horizon optimal bidding strategy. We show that in steady state this optimal strategy generalizes a previous result for equilibrium bidding strategy in “one-shot” auctions.