Keyword Auctions with Budget-constrained Bidders

We study a keyword auction model where bidders have constrained budgets. In the absence of budget constraints, Edelman, Ostrovsky, and Schwarz (2007) and Varian (2007) analyze “locally envy-free equilibrium” or “symmetric Nash equilibrium” bidding strategies in generalized second-price (GSP) auctions. However, bidders often have to set their daily budgets when they participate in an auction; once a bidder’s payment reaches his budget, he drops out of the auction. This raises an important strategic issue that has been overlooked in the previous literature: Bidders may change their bids to inflict higher prices on their competitors because under GSP, the per-click price paid by a bidder is the next highest bid. We provide budget thresholds under which equilibria analyzed in Edelman, Ostrovsky, and Schwarz (2007) and Varian (2007) are sustained as “equilibria with budget constraints” in our setting. We then consider a simple environment with one position and two bidders and show that a search engine’s revenue with budget constraints may be larger than its revenue without budget constraints.